Page 300 - Start Up Mathematics_8 (Non CCE)

ˆ
2
5 ¥
\ Volume of oil tank = pr h = Ê 22 ¥ () 2 30 dm 3
˜
Á
¯
Ë
7
3
= Ê 22 ¥ 25 30¥ ˆ ˜ ¯ dm = 2,357.14 dm 3
Á
Ë
7
3
Hence, the volume of the oil tank is 2,357.14 dm .
7
Example 43: A cylinder whose height is times its diameter, has the same volume as a cube of side 4 cm.
44
Find the radius of the base of the cylinder.
Solution: Let the radius of the base of the cylinder be r cm, then the diameter = 2r cm.
7 7
Let the height of the cylinder be h cm, then h = 44 (2r) = 22 r.
2
2
Volume of cylinder = pr h = 22 × r × 7 r = r 3
7 22
3
3
3
Volume of cube = (Edge) = (4) cm = 64 cm 3
Since, volume of cylinder = volume of cube
3
3
r = 64 fi r = 64 = 4
Hence, the radius of the base of the cylinder = 4 cm
EXERCISE 18.4

1. Find the volume of a cylinder with radius of base = 0.2 m and height = 1.4 m.
2. How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the
water flows at a speed of 30 km per hour?
2
3
3. The curved surface area of a cylinder is 1,320 cm and its volume is 2,640 cm , find its height.
3
4. Find the cost of digging a well 2 m in radius and 14 m deep at the rate of ` 4.80 per m .
3
5. The volume of one metre iron rod is 1,386 cm . Find its diameter.
6. A rectangular sheet of paper, 44 cm long and 16 cm broad, is rolled along its length to form a cylinder.
What is the radius of the cylinder? What is its volume?
7. The thickness of a metal pipe is 1 cm. Its inner diameter is 14 cm. What is the volume of metal
needed for a pipe of length 1 m? (Use π = 3.14)
8. How many cubic metre of soil must be dug out to sink a well which is 21 m deep and has a diameter
of 8 m? If the soil so dug out is spread over a rectangular plot 24 m × 11 m, what is the height of
the platform formed?
9. A particular brand of milk powder is available in two packs—a tin pack with a square base of each side
6 cm and height 14 cm or one with a circular base of radius 3.5 cm and height 12 cm. Which tin has
a greater capacity and by how much?
10. Into a circular drum of radius 4.9 m and height 3.6 m, how many full bags of grain can be emptied
3
if the space required for each given bag is 1.8 m ? (Take π = 3.14)
11. The inner diameter of a wooden cylindrical pipe is 24 cm and its outer diameter is 28 cm. The length
3
of the pipe is 35 cm. Find the mass of the pipe, if 1 cm of wood has mass of 4 g.
2
12. If the lateral surface of a cylinder of height 5 cm is 94.2 cm , then find the:
(a) radius of the base (b) volume of the cylinder (Use π = 3.14)
13. The ratio between the curved surface area and the total surface area of a right circular cylinder is
2
1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm .

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