class 9 prism and room

EX 3 and 4 5:11 PM

Sunday, February 28, 2021

8) height of room=5
area of square=36
area of square=

36=

l=6
b=6
area of 4 wall= 2h( l+b)

=

9) height of room=5
perimeter of room=26
2(l+b)=26

area of 4 wall= 2h( l+b)

=

=

l=6
b=5
we have
area of 4 wall and celling = 107

12
l= 8

area of room=
area of room=48
total cost =

=

13 ) breadth is twice of height
b=2h
length is twice of breadth
l=2b

3 mensuration Page 1

l=2b
l=2

rate of carpeting=500
total cost =64000
we have
total cost =
64000=

area = 128

h= 4
l=4h=16
b=2h= 8
area of 4 wall= 2h( l+b)

=

=192

total cost=
=

14) length is 2 times breadth

length is 5 times height

we have
volume( V) =

800=
800=

8000=

l=20
b=

area of 4 wall=

total cost =

15) length is 3 times of breadth
l= 3b
height of room=4.6
cost of carpeting =1800
rate of carpeting= 240
rate of coloring= 24

3 mensuration Page 2

cost of carpeting=

area = 75

area=
75=

b=5

l=3b=15

area of 4 wall=

cost of coloring =
Page 150

Solution
Height of room (h) =4

b=

Cost of plastering its four wall=640
Rate of plastering ( R)=5
We have
Total cost =
640 =
Area=

Area of 4 wall =
160=

20=

l=15
b=
Area of floor =

=15

Cost of carpeting its floor =
=

3 mensuration Page 3

Cost of carpeting =Rate
7200 =90

Length is 5 less then new length is
3600 =90
Area =40

80-5b=40
40=5b
b=8
From I
l=10

l=12 b=10 , h=6
Area of Room =

=
=

Area of door =
Area of window=
Area of four wall excluding door and window =

=256.5
Total cost = Area

Exercise 4 page 162, 163

Area of trapezium=-

3 mensuration Page 4

Area of trapezium=-

=36

Volume of solid =
=

Find the volume

Area of cross section =9
=243

Volume of solid =
=
=6561

Find the total surface area of figure
Find The volume of prism

Area of cross section =
=100

Perimeter of the cross section = 15+5+5+5+5+5+5
=45

Total surface area of the figure =2

=

3 mensuration Page 5

=
=740

Solution
Area of base =
In Right angle triangle using Pythagoras theorem

Perimeter of triangle = 3+4+5 500 find its height .
=12

TSA of the figure =2

=2
=132

page 162

5 a) A prism has base area 50
solution
Area of base = 50
Volume =500
we have

Height

3 mensuration Page 6

Height

Q a) find the volume of prism formed by joining end to end of cube of length
6 cm
solution
Side of cube (l) = 6cm
Volume of cube =

=
=216
volume of 2 cube =

Q7

Area of cross section =
=36

Volume of prism =

540 =
a=15

10 a) Volume of the triangular prism =864
sides of right angle triangle containing the right angle are 8 cm and 6 cm
Area of Right angle triangle =

=36

Volume of prism =
864 =

Height =

Q 11) Area of the base =

=24

Height of prism =x

Volume of prism =
360 =

x=15

3 mensuration Page 7

x=15
Q 12
Area of rectangular faces=900
Sides of right angle continuing right angle are 9 and 12

h=15
perimeter of triangle = 9+12+15

=36

Height of prism =

13 a)
find the cross section area lateral surface area ,total surface area and volume of a
triangular prism whose sides of base area 4,13, 15 cm and length 20
solution
Solution
Sides of right angle triangle are 4,13,15 respectively
we have,

area of the base =

=
Perimeter of the triangle = 4+13+15

=32
Latera surface area =

=

Total surface area = latera surce area

Volume of Prism =
=

14 a) The length of a prism having right angled isosceles triangular base is 100 cm

3 mensuration Page 8

14 a) The length of a prism having right angled isosceles triangular base is 100 cm
volume 12000 cubic cm find the measures of the base
solution
we have
Volume of the prism = Area of base height
12000=Area of base 100
Area of base =120

Being isosceles triangle p=b

b=
Area of base is Right angle triangle so using Pythagoras theorem

h=
8 a) l=12
sides of right isosceles triangle are

area of triangular base=

=36
LSA of triangular prism =

=(

TSA of triangular prism =

volume of triangular prism=

16a) find the cross section area lateral surface area ,total surface area and volume of a
triangular prism having length 28 cm and measurement of right angled triangular base
sides 10 cm 8 cm and 6 cm respectively
Solution
Sides of right angle triangle are 10 ,8,6
area of the base =

3 mensuration Page 9

Perimeter of the triangle = 10+8+6 latera surce area
=24

Latera surface area =
=

Total surface area =

17 a) find the cross section area lateral surface area ,total surface area and volume of
a triangular prism having length 28 cm and measurement of triangular base sides 6 ,
25, and 29 cm respectively
solution
Solution
Sides of right angle triangle are 6,25,29 respectively
we have,

area of the base =

=

Perimeter of the triangle = 6+25+29
=60

Latera surface area =
=

Total surface area = latera surce area

Area of trapezium=-

3 mensuration Page 10

=36

Volume of solid =
=

Find the volume

Area of cross section =9
=243

Volume of solid =
=
=6561

Find the total surface area of figure
Find The volume of prism

Area of cross section =
=100

Perimeter of the cross section = 15+5+5+5+5+5+5
=45

Total surface area of the figure =2
=
=740

3 mensuration Page 11

Solution
Area of base =
In Right angle triangle using Pythagoras theorem

Perimeter of triangle = 3+4+5 500 find its height .
=12

TSA of the figure =2

=2
=132

page 162

5 a) A prism has base area 50
solution
Area of base = 50
Volume =500
we have

Height

Q a) find the volume of prism formed by joining end to end of cube of length
6 cm
solution
Side of cube (l) = 6cm

3 mensuration Page 12

Side of cube (l) = 6cm
Volume of cube =

=
=216
volume of 2 cube =

Q7

Area of cross section =
=36

Volume of prism =

540 =
a=15

10 a) Volume of the triangular prism =864
sides of right angle triangle containing the right angle are 8 cm and 6 cm
Area of Right angle triangle =

=36

Volume of prism =
864 =

Height =

Q 11) Area of the base =

=24

Height of prism =x

Volume of prism =
360 =

x=15
Q 12
Area of rectangular faces=900
Sides of right angle continuing right angle are 9 and 12

3 mensuration Page 13

h=15
perimeter of triangle = 9+12+15

=36
Height of prism =

3 mensuration Page 14