Vedanta Excel in Mathematics Books 4 Final (2079)

Measurement: Length, Weight and Capacity

14. Let’s measure the length of the following objects.

Objects Length in cm and mm
Your pencil
Your eraser
Your instrument box
Your thumb

15. Let's ask your parents or teachers and estimate,
a) distance between your house and school in km,
b) a place which is about 3 km away from your school,
c) distance between your house and the nearest hospital or health post.
8.4 Addition and subtraction of lengths

Classwork - Exercise

1. Let's add and regroup into the higher units. 14 mm = 10 mm + 4 mm
= 1 cm 4 mm
6 mm + 8 mm = 14 mm = 1 cm 4 mm 120 cm = 100 cm + 20 cm
70 cm + 50 cm = 120 cm = 1 m 20 cm = 1 m 20 cm
580 m + 940 m = 1520 m = 1 km 520 m

a) 4 mm + 9 mm = =

b) 7 mm + 8 mm = =

c) 60 cm + 80 cm = =

d) 90 cm + 45 cm = =

e) 500 m + 700 m = =

f) 650 m + 860 m = =

2. Let's convert the higher units into the lower units, then subtract.

1 cm – 6 mm = 10 mm – 6 mm = 4 mm I've remembered!
1 cm = 10 mm
1 m – 25 cm = 100 cm – 25 cm = 75 cm 1 m = 100 cm
1 km – 540 m = 1000 m – 540 = 460 m 1 km = 1000 m!!

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Measurement: Length, Weight and Capacity

a) 1 cm – 4 mm = =

b) 1 m – 60 cm = =

c) 1 km – 200 m = =

Now, let's learn more about addition and subtraction of length from the
following examples.

Example 1: Add a) 12 cm 6 mm + 10 cm 8 mm

b) 25 m 40 cm + 14 m 75 cm

Solution

a) 121 cm 6 mm I got it!
+ 10 cm 8 mm 6 mm + 8 mm = 14 mm and
14 mm = 1 cm 4 mm
So, 1 cm is carried over to cm!!

22 cm 14 mm

= 23 cm 4 mm

Let's learn this addition converting into the decimals.

12 cm 6 mm = 12 . 6 cm 12 cm 6 mm = 12 cm + 6 cm
10 cm 8 mm = + 10 . 8 cm 10
23 . 4 cm = 12.6 cm

b) 251 m 40 cm 10 cm 8 mm = 10 cm + 8 cm
+ 14 m 75 cm 10
39 m 115 cm
= 10.8 cm

I understood!
40 cm + 75 cm = 115 cm = 1 m 15 cm
So, 1 m is carried over to metre columns!!

= 40 m 15 cm

Again, let's learn this addition converting into the decimals.

25 m 40 cm = 25 . 40 m 25 m 40 cm = 25 m + 40 cm
100
14 m 75 cm = + 14 . 75 m
40.15 m = 25.40 m

14 m 75 cm = 14 m + 75 m
100

= 14.75 m

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Measurement: Length, Weight and Capacity

Example 2: Subtract 9 km 420 m – 5 km 600 m

Solution

1 km = 1000 m Subtraction by converting into decimal

8 1420 9 km 420 m = 9.420 km

9 km 420 m 5 km 600 m = – 5.600 km
– 5 km 600 mm 3.820 km
3 km 820 m

Exercise - 8.2

Section A - Classwork

1. Let's add and regroup into the higher units.

a) 3 mm + 7 mm = mm = cm

b) 20 cm + 80 cm = cm = m

c) 400 m + 600 m = m = km

d) 6 mm + 9 mm = mm = cm mm

e) 50 cm + 70 cm = cm = m cm

f) 500 m + 800 m = m = km m

2. Let's convert into the lower units, then subtract.

a) 1 cm – 5 mm = mm – 5 mm = mm

b) 1 m – 60 cm = cm – 60 cm = cm
c) 1 km – 800 m = m – 800 m = m

Section B

3. Let's add. b) 7 cm 5 mm c) 10 m 60 cm
a) 6 cm 3 mm

+ 4 cm 5 mm + 8 cm 9 mm + 9 m 50 cm

d) 30 m 75 cm e) 12 km 327 m f) 20 km 640 m
+ 24 m 55 cm + 18 km 473 m + 54 km 895 m

151Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

4. Let's subtract. b) 15 cm 3 mm c) 17 m 40 cm
a) 8 cm 7 mm – 10 cm 5 mm – 12 m 25 cm
– 3 cm 4 mm

d) 40 m 35 cm e) 7 km 670 m f) 25 km 345 m
– 24 m 60 cm – 4 km 480 m – 14 km 560 m

5. Let's convert into the decimal of higher units, then add or subtract.

a) 7 cm 5 mm + 5 cm + 8 mm b) 10 cm 6 mm + 14 cm 9 mm

c) 8 m 65 cm + 11 m 76 cm d) 36 m 80 cm + 23 m 75 cm

e) 4 km 570 m + 5 km 590 m f) 16 km 750 m + 20 km 880 m

g) 9 cm 4 mm – 6 cm 5 mm h) 13 cm 6 mm – 7 cm 8 mm

i) 8 m 32 cm – 4 m 40 cm j) 45 m 50 cm – 15 m 90 cm

k) 10 km 300 m – 5 km 500 m l) 54 km 460 m – 28 km 750 m

Let's read these problems carefully and solve them.

6. a) Bamboo is known as one of the fastest growing plants. A bamboo plant
is 3 m 400 cm high on a day. If it grows by 85 cm in one day, what is the
new height of the plant next day?

b) A rubber is 10 cm 6 mm long. If you stretch it by 4 cm 7 mm, what is the
length of the stretched rubber?

c) A book is 1.8 cm thick and another book is 1.4 cm thick. When these
two books are placed one above another, find the total thickness of two
books.

d) The height of a cupboard inside a room is 2.75 m. The ceiling of the room
is 1.86 m above the top of the cupboard. Find the height of the room.

e) Of the total road distance between two villages, 3 km 570 m is blacktop
and the remaining 2 km 685 m is gravelled road. Find the distance
between these two villages.

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Measurement: Length, Weight and Capacity

7. a) The total length of a small fish is 15 cm 3 mm and it's tail is 2 cm 4 mm.
Find the length of the fish excluding the length of its tail.

b) In the long-jump event on a Sport Day, Sahayata jumped 1 m 90 cm and
Sayad jumped 2 m 10 cm. By how much did Sayad win to Sahayata?

c) When a rubber is stretched by 8.6 cm, it's length becomes 20.4 cm. Find
the original length of the rubber.

d) The whole height of an electric pole is 12.35 m. The length of its
underground part is 1.5 m. Find the height of the pole above the ground.

e) A road between two villages is 36 km 280 m long. The part of
20 km 500 m of the road is constructed by the Local Government and
the remaining part is by the Public effort. Find the distance of the road
constructed by the public.

It's your time - Project work!
8. a) Let's measure the length and breadth of your mathematics book by using

a 30 cm - scale. Find by how much is the length longer than the breadth.

b) Lets measure the thickness of your mathematics and English book by
using a ruler.

(i) Find which book is thicker and by how much?

(ii) If you place one book above the another, what is the total thickness?

c) Let's measure the length and breadth of your desk (or table)by using a
measuring tape.

(i) Find the total of the length and breadth.

(ii) Find the difference of the length and breadth.

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Measurement: Length, Weight and Capacity

8.5 Map and distance

Exercise - 8.3
Section A - Classwork
1. Let's read the map of our country Nepal. Tell and write the directions of

different places as quickly as possible.

North

West East

Jumla South

Dhangadhi Jomsom

Nepalgunj Pokhara

Butwal Kathmandu Charikot
Bhaktapur

Birgunj Kalaiya Ilam

Janakpur Dharan Damak

Biratnagar



North, south, east, west, north-east, north-west, south-east, south-west

a) In which direction is Nepalganj from Kathmandu? It is in south-west.

b) In which direction is Dharan from Pokhara? It is in

c) In which direction is Jomsom from Birganj? It is in

d) What is the direction of Dhangadhi from Jumla? It is in

e) What is the direction of Ilam from Biratnagar? It is in

f) In which direction is your home from your school? It is in

2. a) Which place is nearest from Janakpur? Butwal or Damak?

b) Which place is farther from Bhaktapur? Charikot or Kalaiya?

c) Which one is nearer from your home, your school or health post?



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Measurement: Length, Weight and Capacity

Section B

3. Let's read the given road-map distance between different places of far

western provinces of Nepal. Then calculate the distance between the places.

Dadeldhura Surkhet

Bhimdatta (Karnali)
135.18 km

Chisapani
98.43 km
47.54 km Attariya 69.85 km 75.78 km Kohalpur

19.32 km
13.67 km

Dhangadhi Nepalganj

a) Calculate the road distance between Bhimdatta to Dhangadhi.

b) Find the road distance between Dadeldhura and Chisapani.

c) How far is Kohalpur from Attariya?

d) Calculate the road distance from Chisapani to Surkhet.

e) Calculate the road distance from Surkhet to Nepalganj.

4. a) Itahari is 86.46 km west from Chandragadhi and Lahan is 103.68 km
west from Itahari. Find the distance between Chandragadhi and Lahan.

b) Dhulikhel is 105.15 km north-west from Sindhuli and Kathmandu is
32.47 km north-west from Dhulikhel. Calculate the distance between
Sindhuli to Kathmandu.

c) Bhratpur is 162.35 km east from Lumbini and Hetauda is 76.74 km east
from Bharatpur. How far is Hetauda from Lumbini?

It's your time - Project work!

5. a) Let's draw a map of Nepal in a chart paper and show 7 provinces with
different colours.

b) (i) Let's locate one of the famous places or cities in each province. (You
can get help from the original map or google map, etc.)

(ii) Let's visit to the available website (such as www.google.com) and
search the distance between those places or cities. Mention your
findings in the same chart paper.

(iii) In which directions are those places or cities from your place? Which
one is the nearest place to you?

155Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

8.6 Measurement of weight – Looking Back

Facts to remember!
(i) A heavier object has more weight than a lighter object.
(ii) Quintal, Kilogram and gram are the units of measurement of weight.
(iii) Gram is smaller unit and kilogram is higher unit.
(iv) We write kilogram as Kg and gram as g
(v) 1000 g = 1 kg, 2000 g = 2 kg, 3000 g = 3 kg and so on.
(vi) 1 quintal = 100 kg, 2 quintals = 200 kg, and so on.

Classwork - Exercise
1. Let’s guess which object is heavier or lighter. Write the appropriate

words to complete the sentences.
a) A book is heavier than a pencil.

The book has more weight than that of the pencil.

b) An instrument box is than an eraser.

The box has than that of the eraser.

c) A mobile is than a laptop

The mobile has than that of the laptop.

2. Let’s read the measurements of the given weights and find the totals of

kilograms (kg) and grams (g).
a) b)

2 kg 500g 1 kg 2 kg

2 kg 500 g

vedanta Excel in Mathematics - Book 4 156 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Measurement: Length, Weight and Capacity

c) d)

2 kg 2 kg 500g 1 kg 5 kg


e)
f)

5 kg 2 kg 1 kg 200g 2 kg 2 kg 500g 200g


3. Let’s choose and circle the better estimate.

a) b) c) 50 grams
2 kilograms 3 kilograms 500 grams

200 grams 30 grams

d) e) f) 10 kilogram
40 kilograms 1 kilograms 1000 grams
400 grams 10 grams

4. Let’s draw the pointers in the dial balances to show the weights kept
on each balance.

a) b) c)

157Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

5. Let’s write the weight of each object placed on the dial balances.

a) b) c)



8.7 g]kfnL k/Dk/fut tf}nsf OsfO{
gk] fndf tfn} ;DalGw ljleGg k/Dk/fut :yflgo OsfOx{ ¿sf] ko| fu] ug{] ul/G5 .
tfn] f, kfp, ;]/, wfgL{, OToflb tf}nsf sx] L :yfgLo OsfOx{ ¿ x'g\ .

Facts to remember!

(i) 1 tf]nf = 11 g 660 mg (11.66 g)
(ii) 1 kfp = 199 g (nueu 200 g)
(iii) 1 ;/] = 9331 g (nueu 1 kg)
(iv) 1 wfgL{ = 2 kg 393 g (nueu 2 kg 400 g)

6. tnsf kZ| gx¿sf] ;xL pQ/ lbg'xf];\ .

a) cfdfn] ;'g k;naf6 1 tf]nf ;g' lsGg' eP5 . cfdfn] nueu slt u|fd
;'g lsGg' eP5 t < =================================================

b) aa'\ fn] t/sf/L k;naf6 1 kfp Rofpm lsGg' eP5 . a'afn] nueu slt u|fd
Rofpm lsGg' eP5 < =================================================

c) 1 ;]/ rfdn lsGbf slt u|fd rfdn xb' f]/x]5 < ===============================

d) 2 wfgL{ cfn' lsGbf nueu slt lsnfu] f| d / u|fd cfn' x'g] /x5] < ==================

vedanta Excel in Mathematics - Book 4 158 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Measurement: Length, Weight and Capacity

7. Let's say and write which one is a pan balance, spring balance, or a dial
balance.


A balance A
balance A balance

A heavier object has more weight than a lighter
object. We use quintal (q) and kilogram (kg)
unit to measure the weight of heavy objects.
We use gram (g) unit to measure the weight of
lighter objects.

8.8 Conversion of units of weight

Let's remember the following relationship between kilogram (kg), gram (g)
and quintal.

1 kg = 1000 g 1000 g = 1 kg
2 kg = 2 × 1000 g = 2000 g
3 kg = 3 × 1000 g = 3000 g 1 g = 1 g = 0.001 kg
And so on... 1000

kg × 1000 g 48 g = 48 g = 0.048 kg
1000

1 quintal = 100 kg 250 g = 250 g = 0.250 kg
1000

And so on... = 0.25 kg

g ÷ 1000 kg

2 quintals = 2 × 100 kg = 200 kg

3 quintals = 3 ×100 kg = 300 kg and so on.

quintal × 100 kg



159Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

Let's learn more about the conversion of units of weight from the following
examples:

Example 1: Convert a) 2 kg 340 g into grams (g)

b) 3 kg 575 g into kilograms (kg)
Solution

a) 2 kg 340 g = 2 × 1000 g + 340 g I got it!

= 2000 g +340 g 1 kg = 1000 g
So, 2 kg = 2 × 1000 g = 2000 g !!

= 2340 g

I also understood it!

575 1g = (1 ÷ 1000) kg or 1 kg
1000 1000
b) 3 kg 575 g = 3 kg + kg 575
So, 575 g = 1000 kg = 0.575 kg !!

= 3 kg + 0.575 kg

= 3.575 kg

Example 2: Convert 1750 into kg and g I have remembered!
Solution 1000 g = 1 kg!!

1750 g = 1000 g + 750 g

= 1 kg +750 g

= 1 kg 750 g

Example 3: Convert: a) 5 quintals into kilograms (kg)
b) 325 kilograms into quintals and kg
Solution
a) 5 quintals = 5 × 100 kg

= 500 kg I have remembered!
b) 325 kg = 300 kg + 25 kg 1 quintal = 100 kg!!

= 3 quintals 25 kg

vedanta Excel in Mathematics - Book 4 160 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Measurement: Length, Weight and Capacity

Exercise - 8.4
Section A - Classwork
1. Let's say and write how many grams (g).

a) 1 kg = b) 4 kg = c) 5 kg =

d) 0.265 kg = e) 0.325 kg = f) 3.550 kg =

2. Let's say and write how many kilograms (kg).

a) 1000 g = b) 3000 g = c) 6000 g =

d) 215 g = e) 478 g = f) 1236 g =

3. Let's say and write how many kilograms (kg) and grams (g).

a) 1.276 kg = kg g b) 1.036 kg = kg g

c) 2.480 kg = kg g d) 3.5 kg = kg g

4. These are the common weights that we use in our daily lives. Let's say
and write the answer of the following questions.

a) How many 50 g weights make 200 g?

b) How many 100 g weights make 500 g?

c) How many 500 g weights make 1 kg?

d) How many 2 kg weights make 6 kg?

e) Father said that he bought 1.5 kg of vegetables. How many kilograms

and grams vegetables did he buy? kg g

f) Mother said that she bought 2.25 kg of fruits. How many kilograms and

grams of fruits did she buy? kg g

g) A grocer said that he sold 10 quintals of rice in the last month. How

many kilograms of rice did he sell in the last month? kg

161Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

Section B

5. Let's convert the units of weight as indicated.

a) 5 kg (into g) b) 1 kg 200 g (into g)

c) 2 kg 750 g (into g) d) 3 kg 500 g (into g)

e) 15 g (into kg) f) 125 g (into kg)

g) 1 kg 300 g (into kg) h) 2 kg 685 g (into kg)

i) 2 quintals (into kg) j) 7 quintals 40 kg (into kg)

k) 400 kg (into quintals) l) 660 kg (into quintals and kg)

6. Let's convert these grams (g) into kilograms (kg) and grams (g).

a) 1250 g b) 1300 g c) 1500 g d) 1750 g

e) 2100 g f) 2460 g g) 2550 g h) 3225 g

It's your time - Project work!

7. Let's say and write any three pairs of objects, one is heavier and another
is lighter.

a) is heavier and is lighter.

b) is heavier and is lighter.

c) is heavier and is lighter.

8. Let’s measure the weight of the following items using available balances
(pan-balance, digital balance, dial balance, spring blance, etc.). Write the

weight of the items in the table.

Items Kilogram (kg) Gram (g)

Excel in Mathematics book 4

Your instrument box

Your empty school bag

Your school bag with books 162 Approved by Curriculum Development CentreSanothimi, Bhaktapur
and other stationeries

vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

8.9 Addition and subtraction of weights
Classwork - Exercise

1. Let's add and regroup into higher units.

a) 500 g + 600 g = 1100 g = 1 kg 100 g

b) 400 g + 800 g = =

c) 600 g + 700 g = =

d) 800 g + 900 g = =

e) 90 kg + 50 kg = = quintal kg

2. Let's convert into lower unit and subtract.

a) 1 kg – 200 g = 1000 g – 200 g = 800 g

b) 1 kg – 300 g = =

c) 1 kg – 250 g = =

d) 1 kg – 500 g = =

e) 1 quintal – 60 kg = =

Now, let's learn more about addition and subtraction of weights from the
following examples.

Example 1: Add 3 kg 560 g + 2 kg 780 g.
Solution

1 I understood!
560 g + 780 g = 1340 g = 1 kg 340 g
3 kg 560 g
+ 2 kg 780 g So, 1 kg is carried over to kg column.
5 kg 1340 g
= 6 kg 340 g

163Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

Let's learn this addition converting into the decimals of kg.

3 kg 560 g = 3 . 560 kg 3 kg 560 g = 3 kg + 560 kg
1000
2 kg 780 g = + 2 . 780 kg
6 . 340 kg = 3.560 kg

2 kg 780 g = 2 kg + 780 kg
1000

= 2.780 kg

Example 2: Add 2 quintals 75 kg + 4 quintals 60 kg

Solution: It's easier!
135 kg = 100 kg + 35 kg
1
= 1 quintal 35 kg
2 quintals 75 kg

+ 4 quintals 60 kg

6 quintals 135 kg

= 7 quintals 35 kg

Example 3: Subtract 10 kg 250 g – 4 kg 500 g

Solution: Subtracting by converting into decimal

1 kg = 1000 g 10 kg 250 g = 10.250 kg
9 1250
4 kg 500 g = – 4.500 kg
10 kg 250 g
– 4 kg 500 g 5 . 750 kg
5 kg 750 g

Exercise - 8.5
Section A - Classwork
1. Let's say and write the sums or differences as quickly as possible.

a) 500 g + 800 g = g = kg g

b) 400 g + 750 g = g = kg g

c) 70 kg + 80 kg = kg = quanital kg

d) 1 kg – 300 g = g – 300 g = g

e) 1 kg – 550 g = = g

f) 1 quintal – 90 kg = = kg

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Measurement: Length, Weight and Capacity

Let's read the following statements carefully. Then, tell and write the
appropriate weights in the empty circles.

2. a) Priyasha has a 5 kg weight and a 1kg weight. How does she weigh 4 kg of
fruits using her balance just one time?

Fruits Weight Weight
kg 5 kg



b) Nirjal has 5 kg weight and a 2 kg weight. How does he weigh 3 kg of
potatoes using his balance just one time?

Potatoes Weight Weight
kg 5 kg



c) Sunayana has a 10 kg weight, 1 kg weight, and a 2 kg weight. How does
she weigh 7 kg of rice using her balance just one time?

Rice Weight Weight Weight
kg kg kg



3. a) Shreyasha has only a 500 g weight. How does she weigh 1 kg 500 g of
sugar using her balance just two times?

Sugar Weight Sugar Sugar Weight
g 500 g g 500 g 500 g

b) Bishwant has only a 1 kg weight. How does he weigh 3 kg of apples using
his balance just two times?

Apples Weight Apples Apples Weight
kg 1 kg kg kg kg

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Measurement: Length, Weight and Capacity

c) Deejina has a 1 kg weight and a 2 kg weight. How does she weigh 7 kg of
flour using her balance just two times?

Flour weight Weight Flour Flour Weight
kg kg kg 4 kg kg kg

Section B
4. Let's add or subtract.

a) 5 kg 700 g b) 8 kg 650 g c) 10 kg 840 g d) 15 kg 475 g
+ 3 kg 500 g + 7 kg 750 g + 6 kg 690 g + 20 kg 580 g

e) 6 kg 200 g f) 9 kg 550 g g) 12 kg 480 g h) 25 kg 640 g
– 2 kg 300 g – 7 kg 700 g – 6 kg 820 g – 13 kg 960 g

i) 1 q 40 kg j) 5 q 55 kg k) 8 q 50 kg l) 15 q 45 kg
+ 2 q 70 kg + 3 q 85 kg – 4 q 60 kg – 9 q 75 kg

5. Let's convert into the decimal of kilogram, then add or subtract.

a) 4 kg 360 g + 2 kg 790 g b) 7 kg 580 g + 7 kg 840 g

c) 11 kg 720 g + 8 kg 675 g d) 24 kg 900 g + 35 kg 750 g

e) 8 kg 310 g – 3 kg 750 g f) 15 kg 500 g – 8 kg 880 g

g) 20 kg 630 g – 10 kg 570 g h) 36 kg 485 g – 14 kg 655 g

Let's read these problems carefully and solve them.

6. a) Mrs. Kandel bought 2 kg 500 g of cabbage and 3 kg 750 g of potatoes.
Find the total weight of vegetables she bought.

b) Mr. Tharu sold 10 kg 250 g of mangoes yesterday and 15 kg 950 g of
mangoes today. Find the total weight of mangoes he sold in two days.

c) The weight of an empty bag is 275 g. What is the weight of the bag when
it is filled with 4 kg 975 g of potato chips?

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Measurement: Length, Weight and Capacity

d) In a hostel, 5 kg 400 g of rice is consumed at the lunch time and
1 kg 850 g more rice is consumed on the dinner time. How much rice is
consumed at the dinner time?

7. a) A shopkeeper sold 12 kg 600 g of vegetables in the morning and
16 kg 450 g of vegetables in the evening. How much more vegetables did
she sell in the evening?

b) A kangaroo and her joey together have a weight of 72 kg 280 g. If the
mother kangaroo has a weight of 64 kg 540 g, what is the weight of the
joey?

c) The weight of Mr. Motu is 82 kg 510 g and the weight of Mr. patlu is
30 kg 920 g less than the weight of Mr. Motu. Find the weight of Mr. Patlu.

d) Before starting regular cycling Mr. Shrestha had 78 kg 225 g of weight.
After regular cycling for 6 months, he is able to reduce his weight by
7 kg 500 g. How much is his weight now?

8. a) The farmers of a village in Mustang district sold 9 quintals 75 kg of
apples in Aswin month and 6 quintals 45 kg of apples in Kartik month.
How much apples did they sell in two months?

b) The production of rice in a village of Tarai region was 18 quintals
80 kg in the last year and 21 quintals 40 kg this year. By how many
quintals and kilograms was the production of rice increased?

It's your time - Project work!

9. a) Let's measure the weight of your empty bag using any type of balance
available in your school. Also find the weight of each of your textbook,
exercisebook, box, water bottle, etc.

(i) Find the total weight of bags and other items you carry everyday
while coming to school.

(ii) Compare this total weight to your friends' total weight of bags and
other items.

b) Let's make a group of 5 friends of your class. Measure your weights using
a dial balance or a digital balance. Find the difference of your weight
with the weights of your 4 other friends.

167Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

10. a) Let's ask your parents about the estimated quantity of rice that your
family consume in the morning meal and at the dinner. How much rice
does your family consume in (i) 1 day (ii) 7 days (iii) 30 days?

b) Do you know a cup of white rice contains about 53.5 g of carbohydrate?
How much carbohydrate do you consume (i) in 1 day (ii) in 1 month
(iii) in 1 year?

8.10 Measurement of capacity – Looking back

Facts to remember!
(i) The amount of liquid (or gas) that a vessel can hold when it is

filled completely is the capacity of the vessel.
(ii) A bigger vessel has more capacity than a smaller vessel.
(iii) Litre and milliliter are the units of measurement of capacity.
(iv) Litre is bigger unit and millilitre is smaller unit.
(v) We write litre as l and millilitre as ml.
(vi) 1000 ml = 1 l, 2000 ml = 2 l, 6000 ml = 6 l, and so on.

Classwork - Exercise

1. Let’s choose and circle the better estimate: how much liquid do these
vessels may hold?

a) 3 litres b) 4 litres c) 1 litre
5 liters
300 milliliters 400 milliliters

100 millilitres 75 millilitres 200 litres
1 litre 750 millilitres 20 litres

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Measurement: Length, Weight and Capacity

2. Which kind of unit of measurement (litre or millilitre) would you use
to measure the liquids given below?

a) A tea-spoon of medicine millilitre

b) A cup of tea

c) Water in a bucket

d) Milk in a jar

e) A glass of juice

3. Let’s write the amount of liquids in millilitres (ml) shown by the
measuring jars.

a) b) c)

1000 1000 1000
900 900 900
800 800 800
700 700 700
600 600 600
500 500 500
400 400 400
300 300 300
200 200 200
100 100 100

400 ml

4. Given below are 6 measuring jars with different capacities. Let’s use 2
or 3 different jar combinations to fill vessels of the given capacities.

1l

200ml 500 ml

50 ml 100ml

A B C D E
A+C
a) A cup with capacity 250 ml:

169Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

b) A glass with capacity 350 ml:
c) A bottle with capacity 750 ml:
d) A jug with capacity 1 l 650 ml:
e) A bucket with capacity 2 l 500 ml:

8.11 gk] fnL k/Dk/fut Ifdtfsf OsfO{
g]kfndf Ifdtf (Capacity) ;DalGw ljleGg k/Dk/fut :yflgo OsfOx{ ¿sf] klg
ko| f]u ug]{ ul/G5 . dfgf, kfyL, d/' L, OToflb Ifdtf ;DalGw sl] x :yfgLo OsfO{x¿
x'g\ .

Facts to remember!

(i) 1 dfgf = nueu 545 ml (ii) 1 kfyL = nueu 4 l 361 ml
(iii) 1 d/' L = nueu 87 l 215 ml

5. tnsf kZ| gsf] ;xL pQ/ lbgx' f];\ .
a) lbbLn] 8]/Laf6 1 dfgf bw' lsg]/ Nofpg' eof] . lbbLn] nueu slt ml

-ldlnln6/_ bw' lsGg' eP5 t < =================================================

b) a'a\ fn] cfh 1 kfyL £o' a]Rg' eP5 . aa' fn] nueu slt l / ml £o' a]Rg'
eP5 t < =================================================

c) s] tkfOs{ f] 3/kl/jf/df dfgf kfyLsf] k|of]u x'G5 < ===============================

The amount of liquid that a vessel can hold
when it is filled completely is called the

capacity of the vessel.
We use litre (l) to measure the higher

capacity and millilitre (ml) to measure the
less capacity.

We use standard jars of different capacities to measure liquids in litres and
millilitres.

vedanta Excel in Mathematics - Book 4 170 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Measurement: Length, Weight and Capacity

8.12 Conversion of units of capacity

Let's remember the following relationship between litre (l) and
millilitre (ml) .

1 l = 1000 ml 1000 ml = 1 l
2 l = 2 × 1000 ml = 2000 ml
3 l = 3 × 1000 ml = 3000 ml 1 ml = 1 l = 0.001 l
And so on... 1000

l × 1000 ml 55 ml = 55 l = 0.055 l
1000

750 ml = 0.750 l = 0.75 l

And so on... litre
ml ÷ 1000

Let's learn more about the conversion of units of capacity from the following
examples:

Example 1: Convert a) 1 l 250 ml into millilitres (ml)

b) 2 l 180 ml into litres (l) I've remembered!
Solution 1 l = 1 × 1000 ml !!

a) 1 l 250 ml = 1 × 1000 ml + 250 ml

= 1000 ml + 250 ml

= 1250 ml

b) 2 l 180 ml into litres (l) = 2 l + 180 l I got it!
1000
1 ml = (1 ÷ 1000) l or 1 l
1000
= 2 l + 0.180 l 180
So, 180 ml = 1000 l = 0.180 l !!

= 2.180 l

= 2.18 l

Example 2: Convert 2225 ml into l and ml.

Solution

2225 ml = 2000 ml + 225 ml I've remembered!
1000 ml = 1 l
= 2 l + 225 ml 2000 ml = 2 l !!

= 2 l 225 ml

171Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

Exercise - 8.6
Section A - Classwork
1. Let's say and write: how many millilitres (ml).

a) 1 l = b) 5 l = c) 0.180 l =

d) 0.75 l = e) 0.325 l = f) 1.240 l =

2. Let's say and write: how many litres (l).

a) 1000 ml = b) 4000 ml = c) 325 ml =

d) 650 ml = e) 1436 ml = f) 2550 ml =

3. Let's say and write: how many litres (l) and millilitres (ml).

a) 1.175 l = l ml I know it.
b) 2.240 l = l ml 3.5 l means 3.500 l.
It is 3 l 500 ml !!

c) 3.5 l = l ml

d) 4.75 l = l ml

e) Father said that he bought 2.5 l of milk. How many liters and millilitres
of milk did he buy? l ml.

f) Science teacher said that the average adult has bout 4.85 l of blood
circulating inside their body. It is l ml.

Section B

4. Let's convert the units of capacity as indicated.

a) 6 l (into ml) b) 1 l 300 ml (into ml)

c) 2 l 220 ml (into ml) d) 3 l 450 ml (into ml)

e) 36 ml (into l) f) 275 ml (into l)

g) 1 l 180 ml (into l) h) 4 l 625 ml (into l)

5. Let's convert millilitres (ml) into litres (l) and millilitres.

a) 1150 ml b) 1500 ml c) 1890 ml d) 2475 ml

e) 2700 ml f) 3225 ml g) 3570 ml h) 4180 ml

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Measurement: Length, Weight and Capacity

It's your time - Project work!

6. Let's say and write the names of any three pairs of vessels; one holds
more liquid and another holds less liquid.

a) A holds more liquid than a
b) A holds less liquid than a
c) A holds more liquid than a

7. Let’s take a mineral water bottle with capacity 1 l and perform the
following activities in your house.

a) Fill the bottle with water by using your kitchen glass and estimate the
capacity of your glass.

b) Fill the bottle with water by using your tea cup and estimate the
capacity of your tea cup.

c) Fill a pressure cooker with water by using the bottle and estimate the
capacity of the cooker.

8.13 Addition and subtraction of capacities

Classwork - Exercise

1. Let's add millilitres (ml) and regroup into litres (l) and millilitres (ml).

a) 400 ml + 800 ml = 1200 ml = 1 l 200 ml

b) 500 ml + 600 ml = =

c) 750 ml + 700 ml = =

2. Let's convert l into ml, then subtract.

a) 1 l – 100 ml = 1000 ml – 100 ml = 900 ml

b) 1 l – 300 ml = =

c) 1 l – 600 ml = =

Now, let's learn more about addition and subtraction of capacities from the
following examples.

Example 1: Add 2 l 450 ml + 5 l 870 ml

173Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity I got it!
450 ml + 870 ml = 1320 ml = 1 l 320 ml
Solution
So, 1 l is carried over to l column.
1

2 l 450 ml
+ 5 l 870 ml
7 l 1320 ml
= 8 l 320 ml

Let's learn this addition converting into the decimals of l.

2 l 450 ml = 2 . 450 l 2 l 450 ml = 2 l + 450 l = 2.450 l
1000
5 l 870 ml = + 5 . 870 l
5 l 870 ml = 5 l + 870 l = 5.870 l
1000
8 . 320 l

Example 2: Subtract 12 l 300 ml – 7 l 650 ml

Solution: Subtraction by converting into decimal

1 l = 1000 ml

11 1300 12 l 300 ml = 12.300 l

12 l 300 ml 7 l 650 ml = – 7.650 l
– 7 l 650 ml
4 . 650 l

4 l 650 ml

Exercise - 8.7
Section A - Classwork
1. Let's say and write sums or differences as quickly as possible.

a) 600 ml + 500 ml = ml = l ml

b) 350 ml + 850 ml = ml = l ml

c) 1 l – 200 ml = ml – 200 ml = ml

d) 1 l – 750 ml = = ml

2. Let's say and write the capacities of these vessels.

a) A jug is a completely filled with water by a 2l and a 1l jars.
The capacity of the jug is

vedanta Excel in Mathematics - Book 4 174 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Measurement: Length, Weight and Capacity

b) A bottle is completely filled with juice by three 500 ml of jars.
The capacity of the bottle is

c) A bucket is completely filled with water by a 5 l, 2 l, and 500 ml
of jars. The capacity of the bucket is

d) A glass is completely filled with milk by a 200 ml and a 50 ml of
jars. The capacity of the glass is

Section B c) 12 l 580 ml d) 25 l 760 ml
+ 7 l 850 ml + 24 l 940 ml
3. Let's add or subtract.
a) 4 l 300 ml b) 3 l 450 ml

+ 2 l 800 ml + 5 l 750 ml

e) 7 l 100 ml f) 10 l 300 ml g) 14 l 250 ml h) 27 l 840 ml

– 3 l 400 ml – 5 l 500 ml – 10 l 650 ml – 11 l 390 ml

4. Let's convert into the decimal of litres, then add or subtract.

a) 3 l 420 ml + 4 l 860 ml b) 8 l 530 ml + 6 l 970 ml
c) 20 l 355 ml + 15 l 245 ml d) 32 l 675 ml + 17 l 775 ml

e) 9 l 200 ml – 2 l 600 ml f) 18 l 350 ml – 5 l 700 ml

g) 26 l 610 ml – 11 l 450 ml h) 40 l 180 ml – 14 l 360 ml

Let's read these problems carefully and solve them.

5. a) A painter mixed 2 l 500 ml of yellow and 1 l 500 ml of blue paint to make
green paint. How many litres of green paint did he make?

b) 1 l 850 ml of juice is in a jar. When 1 l 650 ml of juice is poured into it, the
jar full. Find the capacity of the jar.

c) In an average, a cow gives 5 l 380 ml of milk in the morning and 4 l 950 ml
of milk in the evening. How much milk does the cow give in a day?

d) A tea-stall owner uses 15 l of milk and 8 l 750 ml of water to make tea
everyday. What amount of tea does she make everyday?

175Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Measurement: Length, Weight and Capacity

6. a) A motorcycle tank contains 15 l 500 ml of petrol when it is full. After
driving a certain distance 6 l 840 ml of petrol is left in the tank. How
much petrol is used up in driving?

b) In a bucket, there is 4 l 520 ml of water. If the capacity of the bucket is
9 l 500 ml, how much more water is needed to fill up the bucket?

c) Mother had 1 l 250 ml of orange juice. She gave two glasses each of
250 ml of juice to me and to my sister.

(i) How much juice did she give us altogether?

(ii) How much juice was left with mother?

d) A dairy had 90 l of milk. It sold 55 l 250 ml of milk in the morning and
25 l 750 ml of milk in the evening.

(i) How much milk did the diary sell in a day?

(ii) How much milk was left in the dairy?

e) A doctor prescribed 10 ml of medicine in the morning and 10 ml in the
evening from a 200 ml bottle of medicine to a patient.

(i) How much medicine did the patient take everyday?
(ii) For how many days is the bottle of medicine sufficient?

It's your time - Project work!

7. Let's take a water bottle of 1 l capacity.

a) Pour as many glasses of water into the bottle as to fill it completely. Now,
estimate the capacity of the glass.

b) Pour as many cups of water into the bottle as to fill it completely. Now,
estimate the capacity of the cup.

8. a) Boys and girls of ages 8 to 12 years need 2.2 l of water everyday. Estimate
how much water do you drink

(i) on 1 day (ii) in 7 days (iii) in 30 days (1 month) (iv) in 1 year?

b) Estimate how much milk do you drink

(i) on 1 day (ii) in 30 days?

c) Estimate how much milk is used in your family

(i) on 1 day (ii) in 30 days?

?

vedanta Excel in Mathematics - Book 4 176 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Unit Measurement - Perimeter, Area and Volume

9

9.1 Perimeter - The distance all the round
Classwork - Exercise

1. Each room of the graphs represents 1 cm length. Let's say and write
how far Popeye has to walk to get round each rectangle.

cm cm cm

cm cm cm


2. Let's add all sides of these plane figures. Then, tell and write the

perimeter of each figure.

a) b) 6 cm

3 cm 3 cm 2 cm 2 cm

6 cm
4 cm
Perimeter of rectangle
Perimeter of triangle

= + + = =+++=

In this way, the distance all the way round is the perimeter of a plane figure.

So, perimeter of a triangle = total of lengths of its 3 sides

Perimeter of a rectangle and square = total of lengths of its 4 sides

177Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

9.2 Perimeter of rectangle and square D l C
Lengths of a rectangle are equal. b
B
So, AB = CD = l (length) b
Breadths of a rectangle are also equal.

So, BC = DA = b (breadth) Al

Perimeter of the rectangle = total lengths of its 4 sides

= AB + BC + CD + DA

= l + b + l + b = 2l + 2b = 2(l + b)
Lengths and breadth of a square are equal.
Sl R It means all 4 sides of a square are equal.
So, PQ = QR = RS = SP = l
ll

P l Q Perimeter of the square = total lengths of its 4 sides

= PQ + QR + RS + SP

= l + l + l + l = 4l

Exercise - 9.1

Section A - Classwork

1. Let's say and write the perimeters of these plane figures as quickly as

possible. 4 cm 2 cm

a) b) c)
2 cm
4 cm 3 cm

3 cm
3 cm
2 cm

5 cm 4 cm 2 cm

Perimeter = cm Perimeter = cm Perimeter = cm

2. Let's say and write the perimeters of these plane shapes as quickly as
possible.

a) Sides of a triangle are 2 cm, 3 cm and 4 cm, perimeter =

b) Sides of a triangle are 5 cm, 4 cm and 6 cm, perimeter =

c) l = 3 cm and b = 2 cm, perimeter of the rectangle =

d) l = 5 cm and b = 3 cm, perimeter of the rectangle =

e) l = 2 cm, perimeter of the square =

f) l = 3 cm, perimeter of the square =

vedanta Excel in Mathematics - Book 4 178 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Perimeter, Area and Volume

3. Perimeter of a rectangle = 2 (l + b). Let's put the value of l and b, then
find the perimeter of rectangle.

a) l = 3 cm, b = 2 cm then 2(l + b) = =

b) l = 4 cm, b = 3 cm, then 2(l + b) = =

c) l = 5 cm, b = 2 cm, then 2(l + b) = =

4. Perimeter of a square = 4 × l. Let's put the value of l, then find the
perimeter of squares.

a) l = 3 cm, then 4 × l = =

b) l = 4 cm, then 4 × l = =

c) l = 5 cm, then 4 × l = =

Section B

5. Let's find the perimeter of the following plane shapes.

a) b) R c) F 2 cm E
3 cm
C
4 cm S D 2 cm C

6 cm 5 cm 4 cm
2 cm
2 cm

A 3 cm B P 4 cm Q A B

4 cm

6. Let's identify whether these figures are rectangle or square. Then, find
their perimeters using the formula 2(l + b) or 4 × l.

a) 3 cm b) 3 cm c) 4 cm

3 cm

3 cm
3 cm
3 cm

2 cm

2 cm

3 cm 3 cm

4 cm

7. a) Let's find the perimeter of triangles whose three sides are:

(i) 4 cm, 5cm, 7 cm (ii) 3.5 cm, 6.5 cm, 8 cm

179Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

b) Let's find the perimeter of rectangles using formula.

(i) l = 5 cm, b = 4 cm (ii) l = 6.5 cm, b = 5.5 cm

c) Let's find the perimeter of squares using formula.

(i) l = 6 cm (ii) l = 8 cm

Let's read these problems carefully, then solve them.

8. a) The rectangular surface of a book is 24 cm long and 24 cm
18 cm breadth. Find the perimeter of the surface.

18 cm

b) The length of a rectangular garden is 60 m and its breadth is 40 m.
Find the perimeter of the garden.

c) A rectangular ground is 150 m long and 110 m wide.

(i) Find the perimeter of the ground.

(ii) If you run around the ground, how many metres do you cover in
one round?

9. a) The length of a square surface of a paper is 12 cm. Find the perimeter
of the surface.

b) A square swimming pool is 75 m long.

(i) Find the perimeter of the pool.

(ii) If you swim round the edges of the pool, how many metres do you
swim in one round?

It's your time - Project work!

10. a) Let's measure the length and breadth of your maths book using a
30 cm - scale. Then, find the perimeter of its surface.

b) Let's measure the length and breadth of your exercise book using a
30 cm - scale. Then, calculate the perimeter of its surface.

c) Let's measure the length and breadth of the surface of your desk
(or table) using a measuring tape. Then, find its perimeter.

d) Let's measure the length and breadth of the surface of white (or black)
board in your classroom. Then, find its perimeter.

Vedanta ICT Corner
Please! Scan this QR code or
browse the link given below:

https://www.geogebra.org/m/pk4xpyxg

vedanta Excel in Mathematics - Book 4 180 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Perimeter, Area and Volume

9.3 Area - Space covered by a surface
Classwork - Exercise

1. Let's observe the surface of these pairs of objects. Write 'G' for the
greater and 'S' for the smaller surface.

a) b) c)


d) e) f)



2. Let's say and write any two pairs of objects inside your classroom: one
has greater and another has smaller surface.

a) A has the greater surface than a

b) A has the smaller surface than a

Do you know? A greater surface covers greater space and it has more area.
A smaller surface covers smaller space and it has less area.

9.4 Area of rectangle and square

In the given square, the length of its each side is 1 cm. 1 cm

The surface of the square covers the space 1 cm length by 1 cm 1 cm

1 cm breadth. 1 cm

So, the area of this square is 1 square centimetre. We write it as 1 sq. cm.

Vedanta ICT Corner
Please! Scan this QR code or
browse the link given below:

https://www.geogebra.org/m/bwjjvd6v

181Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

Classwork - Exercise

1. The area of each square is 1 sq. cm. Let's say and write the area of these

rectangles.

a) b) c)



Area = Area = Area =

2. Each square room represents the area of 1 sq. cm. Let's research and
investigate the formula (rule) to find the area of rectangle.

a) Area of this rectangle = 12 sq. cm.

Number of rooms along length = 4 and along breadth = 3

length × breadth = 4 × 3 = 12 sq.

So, area of rectangle = length × breadth = l × b

b) Area of this rectangle =

Number of rooms along length = and along breadth =

length × breadth = × =

So, area of rectangle = =

c) Area of this rectangle =

Number of rooms along length = and along breadth =

length × breadth = × =

So, area of rectangle = =

In this way, area of a rectangle = length × breadth = l × b

In the case of a square, its length and breadth are equal.
So, area of a square = length × breadth = length × length= l × l

vedanta Excel in Mathematics - Book 4 182 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Perimeter, Area and Volume

Exercise - 9.2

Section A - Classwork

1. The area of each square room of the graph is 1 sq. cm. The area of each
1
half of the square room (triangle) is 2 sq. cm. Let's say and write the
area of these plane shapes.



2. Let's say and write the area of these rectangles or squares as quickly
as possible.
a) b) c)

b = 4 cm
b = 2 cm

b = 3 cm

l = 5 cm l = 2 cm l = 3 cm
Area =
Area = Area =

Section B

3. Let's find the area of rectangles by using formula.

a) l = 5 cm , b = 2 cm b) l = 4 cm, b = 3 cm c) l = 7 cm, b = 4 cm
d) l = 6 cm, b = 5 cm e) l = 8 cm, b = 6 cm f) l = 10 cm, b = 7 cm

4. Let's find the area of squares by using formula.

a) l = 3 cm b) l = 4 cm c) l = 5 cm

d) l = 7 cm e) l = 9 cm f) l = 10 cm

183Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

Let's read these problems carefully, then solve them.

5. a) The rectangular surface of a mobile phone is 9 cm 6 cm
long and 6 cm wide. Find the area of its surface.
9 cm

b) Length of the rectangular surface of a 8 cm
geometry box is 16 cm and its breadth is
8 cm. Find the area of its surface. 16 cm

c) The rectangular floor of a room is 10 m long and 8 m broad. Find the
area of the floor in sq. m.

6. a) The given greeting card is in the shape of a square. 12 cm
Its length is 12 cm. Find the area of the surface of 12 cm
the card.

b) The length of a square pond is 90 m. Find the area of the pond.

c) The given photo frame is in the shape of a square
and it's length is 21 cm. Find the area of the surface
of the frame.

It's your time - Project work!

a) Let's measure the length and breadth of the given objects using a
30 cm -ruler. Then, find the area of the surface of the objects.

Objects Length (l) Breadth (b) Area

Math book

Exercise book

vedanta Excel in Mathematics - Book 4 184 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Perimeter, Area and Volume

b) Let's measure the length and breadth of the surface of the given objects using
a measuring tape. Then, calculate the area of the surface.

Objects Length (l) Breadth (b) Area

Desk

Table
White/black board

Classrooom

9.5 Volume - space occupied by an object

Let's take a full glass of water. Immerse
a stone into the water. Now, let's discuss
the answers of the following questions.

a) What happened when the stone is
immersed into the water?

b) Does the water overflow?
c) What caused the overflow of water?
d) Why did the water overflow?
A stone is a solid object. When it is immersed into water, it occupies same

space in the water. The space is provided by the overflowing water.
The space occupied by a solid object is the volume of the solid object.

9.6 Volume of cube

The given solid is a cube. The length, breadth, and height of

a cube are equal. In the given cube, its length, breadth and 1 cm
1 cm
height are 1 cm each. 1 cm

So, it occupies 1 cube centimetre (cu. cm.) space.

Its volume is 1 cubic centimetre (cu. cm.).

1 cu. cm = 1 cm × 1 cm 1 × cm

= length × breadth × height

185Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Perimeter, Area and Volume

So, the volume of cube = length × breadth × height

= length × length × length

=l×l×l

Cubic centimetre (cu. m.) and cubic metre (cu. m.) are the units of volume.

1 cubic metre (cu. m.) = 1 m × 1 m × 1 m

9.7 Volume of cuboid

The given solid is a cuboid. It is made up of joining 3 cubes. Each cube has
volume of 1 cu. cm. So, the volume of this cuboid is 3 cu. cm.

3 cu. cm = 3 cm × 1 cm × 1 cm 1 cm
= length × breadth × height

=l×b×h 1 cm 1 cm 1 cm 1 cm

Volume of cuboid = l × b × h

Volume of this cuboid = 16 cu. cm

2 cm = 4 cm × 2 cm × 2 cm

4 c m 2c m = length × breadth × height
=l×b×h

Exercise - 9.3

Section A - Classwork

1. Let's say and write which one can occupy more space. Then, write
which one has more volume.

A occupies more space.
A juice box A match box So, has more volume.

A occupies more space.

A laptop A mobile So has more volume.

vedanta Excel in Mathematics - Book 4 186 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Perimeter, Area and Volume

A occupies more space.

So, has more volume.

A geometry box A book

2. Let's say and write the answer as quickly as possible.

a) A cube occupies the space of 8 cu. cm. What is the volume of the

cube?

b) A cubical box occupies the space of 27 cu. cm. What is the volume of the
box?

c) A book occupies the space of 180 cu. cm. What is the volume of the
book?

d) The volume of a cube is 64 cu. cm. How much spaces does it
occupy?

e) The volume of a brick is 720 cu. cm. How much space does it
occupy?

3. Each cube represents a volume of 1 cu. cm. Let's count the number of
cubes. Then tell and write the volume of each solid.
a) b) c)

Volume = Volume = Volume =
d) e) f)

Volume = Volume = Volume =
g) h) i)

Volume = Volume = Volume =

Section B
4. Let's find the volume of cubes by using formula.

a) l = 2 cm b) l = 3 cm c) l = 4 cm d) l = 5 cm

e) l = 6 cm f) l = 7 cm g) l = 10 cm h) l = 12 cm

187Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

5. Let's calculate the volume of cuboids by using formula.
a) l = 4 cm, b = 3 cm, h = 2 cm b) l = 5 cm, b = 4 cm, h = 1 cm
c) l = 6 cm, b = 4 cm, h = 3 cm d) l = 9 cm, b = 5 cm, h = 4 cm
e) l = 10 cm, b = 7 cm, h = 5 cm f) l = 15 cm, b = 10 cm, h = 8 cm
6. Let's calculate the volume of the following solid objects.

a) b) c)

1cm

2cm 10cm
4cm
2cm2cm 10cm 20cm
2 cm 2cm 15cm
10cm

d) e) f)

2cm 3cm 9cm

15 cm 8 cm 5cm

7. a) A cubical die is 3 m long. Find its volume. How much space does it
occupy?

b) A sweet is in the shape of a cube and its length is 2 cm. Find its volume.

How much space does it occupy?

c) A cubical box is 8 cm long. Find its volume. How much space does it

occupy?

8. a) A chocolate bar is 6 cm long, 3 cm wide, and 2 cm thick. Calculate its
volume.

b) A geometry box is 16 cm long, 8 cm wide, and 3 cm high. Find its volume.

c) A book is 24 cm long, 18 cm broad ,and 2 cm thick. Find its volume.

It's your time - Project work!

9. a) Let's measure the length, breadth and thickness of your maths book
using a 30 cm - ruler. Then, find its volume.

b) Let's measure the length and height of your geometry box. Then, find
its volume.

Vedanta ICT Corner
Please! Scan this QR code or
browse the link given below:

https://www.geogebra.org/m/vgzuzjsd

?

vedanta Excel in Mathematics - Book 4 188 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Unit Algebra

10

10.1 Mathematical sentence
Classwork - Exercise

1. Let's rewrite the following statements using mathematical signs.

a) 4 added to 5 is 9. ..................... b) 1 added to 2 is 3. .....................

c) 6 subtracted from 8 is 2. ..................... d) 3 subtraction from 7 is 4. ....................

e) 2 multiplied by 5 is 10. ..................... f) 18 is divided by 6 is 3. .....................

In this way, a mathematical sentence contains mathematical operations.

For example,

2 added to 3 is 5. 2 + 3 = 5, and it is true.

1 subtracted from 10 is 9. 10 – 1 = 9, and it is true.

3 multiplied by 4 is 12. 3 × 4 = 12, and it is true.

15 divided by 5 is 3. 15 ÷ 5 = 3, and it is true.

10.2 Mathematical sentences on addition and subtraction
Classwork - Exercise

1. Let's say the correct number of marbles in each bag. Then, write the
mathematical sentences as shown in the example.

Number of marbles in each bag Mathematical sentences

2+ = 2 +1= 3

+=

+=

+ =

3– = 3 –1 = 2

–=
–=

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2. Let's write the numbers in the boxes. Then, say and write the correct
answer.

a) You have 3 sweets. When mother gives you a few more sweets you have
now 5 sweets. How many sweets does mother give you?

Let's write the numbers 1 and 2 respectively in the box.

3 + 1 = 5 which is not true.

3 + 2 = 5 which is true.

So, 2 is the correct number in the box.

b) Pranave has 5 marbles. When his brother gives him a few more marbles,
he has now 9 marbles. How many marbles does his brother give him?

Let's write the numbers 1, 2, 3 and 4 respectively in the box.

1 5 + = 9 which is not true.

2 5 + = 9 which is not true. Vedanta ICT Corner
which is not true. Please! Scan this QR code or
3 5 + = 9 which is true. browse the link given below:

4 5 + https://www.geogebra.org/m/nsnkuz56

= 9

So, is the correct number in the box.

c) Bhurashi has some oranges. When her father gives her 2 more oranges,
she has now 7 oranges. How many oranges does father give her?

Let's write the numbers 1, 2, 3, 4 and 5 respectively in the box.

+ 2 = 7 which is .

+ 2 = 7 which is .

+ 2 = 7 which is .

+ 2 = 7 which is .

+ 2 = 7 which is .

So, is the correct number in the box.

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d) You have a few pencils. When you give 3 pencils to your friends 1 pencil
is left with you. How many pencils did you have at the beginning?

Let's write the numbers 1, 2, 3 and 4 respectively in the box.

– 3 = 1 which is .
– 3 = 1 which is
– 3 = 1 which is Vedanta ICT Corner

. Please! Scan this QR code or

browse the link given below:

. https://www.geogebra.org/m/euqg92gk

– 3 = 1 which is .

So, is the correct number in the box.

e) Teacher has a few apples. When she gives 1 apple to her student 2 apples
are left with her. How many apples did she have at the beginning?

Let's write the numbers 1, 2 and 3 respectively in the box.

– 1 = 2 which is .

– 1 = 2 which is .

– 1 = 2 which is .

So, is the correct number in the box.

10.3 Mathematical sentences on multiplication and division
Classwork - Exercise

1. Let's write the numbers respectively in the boxes. Then, say and write
the correct answer.

a) You divide 6 pencils equally between your 3 friends. How many pencils
does each friend get?

Let's write the numbers 1 and 2 respectively in the box.

3 × 1 = 6 which is not true.

3 × 2 = 6 which is true.

So, 2 is the correct number in the box.

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b) Teacher divide 12 sweets equally between 4 children. How many sweets
does each child get?

Let's write the numbers 1, 2 and 3 respectively in the box.

4 × = 12 which is .

4 × = 12 which is .

4 × = 12 which is .

So, is the correct number in the box.

c) Mother divides 15 strawberries equally between me and my 2 more
friends. How many strawberries do each of us get?

Let's write the numbers 1, 2, 3, 4 and 5 respectively in the box.

3 × = 15 which is .

3 × = 15 which is .

3 × = 15 which is .

3 × = 15 which is .

3 × = 15 which is .

So, is the correct number in the box.

2. Let's write the numbers in the boxes. Then, say and write the correct
answer.

a) To how many friends can you divide 6 erasers equally so that each friend
gets 3 erasers?

Let's write the numbers 1 and 2 respectively in the box.

6 ÷ 1 = 3 which is not true.

6 ÷ 2 = 3 which is true.

So, 2 is the correct number in the box.

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b) To how many children can your teacher divide 8 marbles, so that each
child gets 2 marbles?

Let's write the numbers 1, 2, 3 and 4 respectively in the box.

8 ÷ = 2 which is .

8 ÷ = 2 which is .

8 ÷ = 2 which is .

8 ÷ = 2 which is .

So, is the correct number in the box.

3. Let's write the numbers in the boxes. Then, say and write the correct
answer.

a) How many pencils can be equally divided between 2 children so that
each can get 2 pencils?

Let's write the numbers 1, 2, 3 and 4 respectively in the box.

1 ÷ 2 = 2 which is not true.

2 ÷ 2 = 2 which is not true.

3 ÷ 2 = 2 which is not true.

4 ÷ 2 = 2 which is true.

So, is the correct number in the box.

b) How many sweets can be equally divided between 3 children so that
each can get 2 sweets?

Let's write the numbers 1, 2, 3, 4, 5 and 6 respectively in the box.

÷ 3 = 2 which is .

÷ 3 = 2 which is .

÷ 3 = 2 which is .

÷ 3 = 2 which is .

÷ 3 = 2 which is .

÷ 3 = 2 which is .

So, is the correct number in the box.

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4. Let's recall the multiplication tables of the numbers from 1 to 10.
Then, say and write the correct number in the box.

a) What number is multiplied by 4 to get the product 20?

× 4 = 20 1 × 4 = 4, 2 × 4 = 8, 3 × 4 = 12, 4 × 4 = 16, 5 × 4 = 20

b) What number is multiplied by 7 to get the product 42? × 7 = 42

c) What number is divided by 5 to get the quotient 7? ÷5 =7

d) What number is divided by 9 to get the quotient 10? ÷ 9 = 10

e) By what number is 48 divided to get the quotient 6? 48 ÷ =6

f) By what number is 80 divided to get the quotient 8? 80 ÷ =8

Exercise - 10.1

Section A - Classwork

1. Let's select and write the correct number in the box to make the
mathematical sentences true.

Mathematical sentence Given numbers

+2=7 1, 2, 3, 4, 5, 6

4 + = 10 1, 2, 3, 4, 5, 6, 7

12 – = 8 1, 2, 3, 4, 5

–3=5 1, 2, 3, 4, 5, 6, 7, 8, 9

× 4 = 16 1, 2, 3, 4, 5

5 × = 30 1, 2, 3, 4, 5, 6, 7

24 ÷ =6 1, 2, 3, 4, 5

÷3=3 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

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Section B

2. Let's write the numbers in the box in order. State whether the
mathematical sentence is 'true' or 'not true' for each number. Then,
find the correct number in the box.

a) 2 + = 5 (Write 1, 2 and 3 respectively in the box.)

b) + 4 = 9 (Write 1, 2, 3, 4 and 5 respectively in the box.)

c) 12 – = 8 (Write 1, 2, 3 and 4 respectively in the box.)

d) – 3 = 7 (Write 1 to 10 respectively in the box.)

e) 5 × = 40 (Write 1 to 8 respectively in the box.)

f) × 9 = 54 (Write 1 to 6 respectively in the box.)

g) 45 ÷ = 9 (Write 1 to 5 respectively in the box.)

h) ÷ 4 = 2 (Write 1 to 8 respectively in the box.)

3. Let's write the correct numbers inside the circles to make the
mathematical sentences true.

a) + 2 = 6 b) + 5 = 8 c) + 4 = 9

d) 4 + = 7 e) 3 + = 8 f) 5 + = 9

g) – 1 = 3 h) – 2 = 7 i) – 7 = 5

j) 4 – = 3 k) 9 – = 7 l) 12 – = 5

m) × 4 = 8 n) × 3 = 9 o) 2 × = 18

p) ÷ 2 = 3 q) ÷ 4 = 2 r) 20 ÷ = 4

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10.4 Mathematical sentence using letters

Let's discuss on the following illustrations.

(i) What should be added to 1 to get 5?

+ 1 = 5 4 + 1 = 5 x+1=5

x + 1 = 5 is a mathematical sentence with the letter x and the value of
x is 4.

(ii) From what is 1 subtracted to get 9?

– 1 = 9 10 – 1 = 9 a–1=9

a – 1 = 9 is a mathematical sentence with the letter a and the value of
a is 10.

(iii) What should be multiplied by 2 to get 6?

2 × = 6 2 × 3 = 6 2×x =6

2 × x = 6 is a mathematical sentence with the letter x and the value of
x is 3.

(iv) What should be divided by 3 to get 4?

÷ 3 = 4 12 ÷ 3 = 4 p÷3=4

p ÷ 3 = 4 is a mathematical sentence with the letter p and the value of
p is 12.

In this way, x + 1 = 5, a – 1 = 9, 2 × x = 6 and p ÷ 3 = 4 are mathematical
sentences with some letters. Such mathematical sentences with letters are
called equations.

We can compare an equation to a pan balance, where the equal sign as the
balance point.

9=9 8+1 = 9 x+1 = 9

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Classwork - Exercise
1. Let's tick (√) the mathematical sentence with letter.

a) 2 added to 7 is 9. b) x added to 5 is 8.

c) 3 times y is 12. d) difference of 5 and 2 is 3.

e) 4 times 5 is 20. f) 6 subtracted from x is 4.

2. Let's make mathematical sentences with the given letters.

a) x added to 3 is 7.
b) The difference of y and 5 is 6.

c) 2 times p is 10.

d) x divided by 3 is 5.

3. Let's list out the equations separately.

x + 2, x + 2 = 5, x – 3, 4x Equations

x – 3 = 7, 4x = 20, x , x = 6
2 2

10.5 Finding the value of letter

Classwork - Exercise

1. Let's say and write the correct number in the box.

2 a) What should be added to 1 to get 3? + 1 = 3

b) What should be added to 2 to get 5? + 2 = 5

c) From what is 1 subtracted to get 2? – 1 = 2

d) From what is 4 subtracted to get 5? – 4 = 5

e) What should be multiplied by 3 to get 9? 3 × = 9

f) What should be multiplied by 5 to get 10? 5 × = 10

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g) What should be divided by 2 to get 3? ÷ 2 = 3

h) What should be divided by 3 to get 5? ÷3=5

2. Let's say and write the correct value of the letters.

a) What should be added to 3 to get 6? x+ 3 = 6
Let's replace x by 1, 2 and 3. Then x =

b) What should be added to 5 to get 9? y+ 5 = 9
Let's replace y by 1, 2, 3 and 4. Then y =

c) From what is 2 subtracted to get 4? a–2=4
Let's replace a by 1, 2, 3, 4, 5 and 6. Then a =

d) From what is 4 subtracted to get 3? p–4=3
Let's replace p by 1, 2, 3, 4 5, 6 and 7. Then p =

e) What should be multiplied by 4 to get 8? 4× b =8
Let's replace b by 1 and 2. Then b =

f) What should be multiplied by 5 to get 15? 5 × c = 15
Let's replace c by 1, 2 and 3. Then c =

g) What should be divided by 2 to get 2? x÷2 =2
Let's replace x by 1, 2, 3 and 4. Then x =

h) What should be divided by 3 to get 1? y÷3 =1
Let's replace y by 1, 2 and 3. Then y =

Now, let's make mathematical sentences using letters. Then, learn to find the
values of the letters.

Example 1: What number is added to 2 to get the sum 7?

Solution

x is added to 2 to get the sum 7. So, x + 2 = 7

5 is added to 2 to get the sum 7. So, x = 7 – 2 = 5

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