cone 5:02 PM
Tuesday, February 2, 2021
7a) determine the volume of the cone having the height 48 cm and slant height 50 cm
solution:
height of the cone (h ) = 48
slant height (l) = 50 cm
we have
Again
we have
Volume of the cone (V)=
8a) the surface area of cone is 550 and its slant height 25 find the height of the cone .
solution
slant height (l) =25
curved surface area (
9a) the total surface are and curved surface area of a cone are 704 and 550 respectively find the
slant heigh of the cone .
solution :
curved surface area (
total surface are (
from( i)
(
10 a) the radius and slant height of the cone are in the ratio of 7: 25 if its curved surface area is
220 find the radius
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220 find the radius
solution :
Ratio of radius and slant height is 7:25
r=7x
l= 25x
curved surface area=
r=
11 a) the ratio of radius of base o f and height of a cone is 5:12 and volume is 314. 29 find the
curved surface area and total surface area.
solution:
Ratio of the radius and height = 5:12
r=5x and h=12x
we have
volume of the cone =
surface area=
total surface area =
12 a) The vertical height of the cone is 3 times the diameter . If the volume of the cone is
find the total surface area .
solution:
The vertical height of the cone is 3 times the diameter
h=3d
h=6r
Volume of the cone (V)=
r=3
h=
Total surface area of cone =
13) if the circumference of a base of a cone is 33 and slant height is 10 cm . Find the curved
surface area for tent
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Solution:
Circumference( c )=
r=
l=10
for cone we have
CSA of the cone =
14) The curved surface area of cone is 550 and diameter of the base is 14 . Find the volume of
the cone
solution:
r=
CSA of cone= 550
l=25
h=24
Volume of the cone=
15) from a cylinder of height 24 cm and base diameter 14 cm a cone having a equal radius and
height is hollowed out . Find the volume of the remaining solid of the cylinder.
solution:
r=
h= 24
Volume of remaining solid = Volume of the cylinder - volume of the cone
=
16) find the volume of the following solid
solution :
Height of cylinder (h1)=30
height of the cone( h)=54-30
slant height (l)= 25
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slant height (l)= 25
for cone we have,
Volume of the solid= Volume of the cone +Volume of the cylinder
=
17a) find the CSA of the given solid
solution :
r=
height of the cylinder (h1)= 27
Height of the cone = 39-27 =12
for cone
CSA of solid= CSA of cylinder+ CSA of Cone
=
=
18 a) find the total surface area of the given solid
solution:
Radius of the base of cylinder ( r) =
height of the cylinder (h1)=140
Height of the cone (h)= 152-140=12
for cone
= 169
l=13
TSA of the solid= area of the base+ CSA of cylinder+ CSA of Cone
=
=
=
19) the base area of the cylinder is 100 cm2 and the height of the cylinder is 3 cm . If the volume
of the whole solid is 500 cm3 . Find the height of the solid
solution:
Area of base of cylinder
height of the cylinder (
volume of the solid= Volume of the cone +volume of the cylinder
500=
500=
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500=
500-300=
200
h=6
total height = h1+h
20) the curved surface area of the given figure is 4686. find the common radius
solution :
slant height of the cone (l)=29
CSA of combine solid=CSA of cone +CAS of hemisphere
4686=
4686=
4686=
21a) the volume of the given solid object is 38808 cm3. find the radius of the base find the volume
of the cone
solution :
Height of cone (h1)= 36
Height of the cylinder (h) = 240
volume of the solid= volume of the cone +volume of the cylinder
38808=
volume of cone=
22 a) if the water filled in the cone is poured into the cylinder , to what height will the surface of
the water reach such that the cone will be full of water
solution:
Radius of cone(r )=
Radius of cylinder (r )=
Height of the cone (h)=10
volume of cone=
=
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=
the water filled in the cone is poured into the cylinder
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combined solid
Tuesday, February 2, 2021 9:24 PM
1a) area of ABCD= Area of ADB +area of
=
total cost =
2a
area of trapezium ABCD=
=
Total cost =
3a) same as 4
4a) the length breadth and height of the a rectangular tank are 5 m 5 m and 4 m respectively . If
1000 liters of water cost Rs 4000 , how much dies the total cost to fill the tank ?
solution :
volume of tank =
So, capacity of tank in liters=
1000 liters of water cost Rs 4000
1 liters of water cost Rs
100000 liters of water cost Rs
7a) A water storage tank is made by using 9 circular rings having diameter 3.5 feet and height 1 feet
How many cubic feet feet of water can be storage in the tank ? What is the cost of making the tank at
the rate of Rs 1300 per ring ? If 1 cubic foot is equivalent 20.317 liters then find the capacity of the
tank in liters
solution :
Radius of cylinder ( r )=
height of the cylinder=
cost of making tank = Rate numbers of ring
=
Volume of tank=
capacity of tank in liters=
8) The adjoining figure are the figures of two pillars with mounted squared pyramid on the dop . Find
the total cost to of painting the pillar at the rate of Rate of 52 per square feet .
Solution :
height of the pyramid (h)= 1
side of the pyramid(a)= 1
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side of the pyramid(a)= 1
we have for pyramid
l=
Area to paint on the one pillar= LSA of pyramid + 4 wall of the pyramid
=
=
cost of painting = area
cost of painging two pillar=
9) A tent is of the shape of a right circular cylinder up to a height of 4 meters and then becomes a
right circular cone with a maximum height of 16 meters above the ground . Calculate the cloth to
cover the tent of the tent at the rate of Rs 100 per square meter , if the radius of the base id 14
solution:
Radius( r ) = 14
height of the cylinder (h1) =4
height of the cone (h)= 16-4 = 12
rate = Rs 100
for cone
there is no tent on base and tent is in the CSA of the combine solid
CSA of the shape= CAS of Cylinder + CSA of cone
=
=
total cost = CAS
10) A cylindrical water tank having radius 210 cm and height 700 cm has hemispherical top . How many
maximum liters of water can the tank hold?
solution :
Radius of cylinder (r )=210
Height of the cylinder ( h) =700
Volume of the tank (V)= volume of the cylinder +Volume of hemisphere
=
=
=
Capacity of tank in litters = Volume of tank
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11a) A cylindrical water tank having diameter 1.4 m and height 1.05 m has a conic top having height
o.36 m How many maximum liters of water can the tank hold?
solution :
dimeter of cylinder (d )=1.4
Radius of cylinder (r )=0.7
Height of cone(h) = 1.05
height of the cylinder (h1)=
volume of the solid = Volume of cone + volume of the
water capity in liters =
12 a) Pemba makes an arrangement for accommodation of 150 guest in his daughters marriage
ceremony . For this purpose he plans to build a conical tent in such away that each person have 4
sq .m of the space on ground and 20 cu.m . Of air to bread . What should be the height of the tent?
Find it
solution:
Area of base=
volume of cone (V)=
we have
volume of cone=
3000=
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