Page 249 - ICSE Math 8

EXERCISE 22.4

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?
3
3. Find the cost of digging a well 2 m in radius and 14 m deep at the rate of ` 4.80 per m .
3
4. The volume of one metre iron rod is 1,386 cm . Find its diameter.
5. 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?
6. 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 p = 3.14)
7. 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?
8. A rectangular sheet of paper 35 cm × 21 cm can be transformed into the curved surface of a right circular
cylinder in two ways, i.e., either by rolling the paper along its length or along its breadth. Find the ratio
of the volumes of the two cylinders thus formed.
9. The circumference of the base of a cylinder is 264 cm and its height is 24 cm. Find the volume of the
cylinder.
10. If the radius of the base of a right circular cylinder is halved keeping the height same, find the ratio of
the volume of the smaller cylinder to that of the original cylinder.

AT A GLANCE

¾ Cuboid Æ Length (l), Breadth (b), Height (h)
(i) Volume (V) of a cuboid = Length × Breadth × Height = l × b × h cubic units
(ii) Total surface area (TSA) of cuboid = 2(lb + bh + hl) sq. units
(iii) Lateral surface area (LSA) or area of four walls of cuboid = 2h(l + b) sq. units
(iv) Length of the diagonal of cuboid = l + 2 b + 2 h units
2
¾ Cube Æ side (or edge) = a units
3
3
(i) Volume of cube = (Side) = a cubic units
2
2
(ii) Total surface area (TSA) of cube = 6 (Side) = 6a sq. units
2
2
(iii) Lateral surface area (LSA) of cube = 4 (Side) = 4a sq. units
(iv) Length of the diagonal of cube = 3 (side) = 3a units
¾ Right Circular Cylinder Æ Radius (r), Height (h)
2
(i) Volume of right circular cylinder = pr h cubic units
(ii) Curved surface area (CSA) of right circular cylinder = 2prh sq. units
(iii) Total surface area (TSA) of right circular cylinder = 2pr(h + r) sq. units
¾ Hollow Cylinder Æ External radius (R), Internal radius (r), Height (h)
2
2
(i) Volume of hollow cylinder = External volume – Internal volume = ph(R – r ) cubic units
2
2
(ii) Surface area of each base = p(R – r ) sq. units
(iii) Curved surface area (CSA) of hollow cylinder = 2ph(R + r) sq. units
(iv) Total surface area (TSA) of hollow cylinder = CSA + Surface area of 2 bases
= 2p(R + r)(h + R – r) sq. units.

237