Page 246 - ICSE Math 8

EXERCISE 22.3

1. The radius of a right circular cylinder is 7 cm and its height is 14 cm. Find its curved surface area and
total surface area.
2
2. The curved surface area of a cylinder is 1,000 cm and the radius of its base is 21 cm. Find the total
surface area of the cylinder.

3. An open cylindrical oil tank has diameter 14 m and height 9 m. If the inner side of the tank has to be
painted all over, what will it cost at ` 40 per square metre?
4. The inner diameter of a circular well is 3.5 m and it is 12 m deep. Find the cost of plastering the inner
surface at the rate of ` 4 per square metre.
5. It costs ` 2,200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If it is painted at the
rate of ` 20 per square metre, find:
(a) the inner curved surface area of the vessel (b) the radius of the base

6. A cylindrical road roller is of length 2 m and diameter 84 cm. Find the number of revolutions it has to
2
make to cover an area of 7,920 m .
7. The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 5 : 3. Find the ratio of
their curved surface areas.
8. Some fruits are sliced and packed into cylindrical cans of height 32 cm and diameter of base 20 cm.
A label is placed around the curved surface of the can by leaving a margin of 2 cm from the top and
bottom of the can. Find the surface area of the label.

9. A school organized a competition of making and decorating pen holders in the shape of a cylinder by
making its base and its curved surface area with cardboard. Each pen holder is supposed to have a radius
of 3.5 cm and height 10 cm. How much cardboard does the school need if 30 students are participating
in the competition?
10. A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm and the outer diameter is
4.8 cm. Find its:
(a) inner curved surface area (b) outer curved surface area (c) total surface area

11. A cylindrical vessel open at the top has a base diameter of 21 cm and height 14 cm. Find the cost of tin
2
plating its inner part at the rate of ` 5 per 100 cm .
Volume of a Cylinder r

Let there be a cylinder with radius r unit and height h unit (Fig. 22.5).
Volume of the right circular cylinder = Area of the base × height h

2
= (pr × h) cubic unit
2
= pr h cubic unit r
Fig. 22.5
Volume of a Hollow Cylinder r

Let there be a hollow cylinder with external and internal radii R and r
respectively and height h (Fig. 22.6). h
Volume of the hollow cylinder = External volume – Internal volume
2
2
= (pR h – pr h) cubic unit R
2
2
= ph(R – r ) cubic unit Fig. 22.6
234