Page 243 - ICSE Math 8

5. Find the volume of a cube whose surface area is:
2
2
2
(a) 54 cm (b) 294 m (c) 384 dm (d) 486 cm 2
6. Three cubes of edges 8 cm are joined end to end. Find the surface area of the resulting cuboid.
7. Find the cost of painting 3 iron boxes at the rate of ` 5 per square metre, whose dimensions are
1.5 m × 0.85 m × 0.20 m, 2 m × 0.65 m × 0.35 m and 2 m × 0.90 m × 0.45 m.
8. The ratio of the surface areas of two cubes is 16 : 25. Find the ratio of their volumes.
9. The perimeter of a floor of a rectangular hall is 60 m and its height is 3 m. Find the cost of painting its
2
four walls at the rate of ` 20 per m .
2
2
10. A cuboid has total surface area of 60 m and lateral surface area of 40 m . Find the area of its base.
11. The length of a hall is 22 m and breadth is 18 m. The sum of the areas of the floor and the flat roof is
equal to the sum of the area of the four walls. Find the height and volume of the hall.
12. A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given
cube and that of one of the cuboids.
13. The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of
2
covering it with a cloth at the rate of ` 10 and ` 11 per m is ` 1,300. Find the dimensions of the box.
14. A rectangular swimming pool 30 m long, 20 m wide and 1.5 m deep is to be tiled. If each tile is
50 cm × 50 cm, how many tiles will be required?
15. A log of wood of dimensions 2 m × 20 cm × 10 cm is cut into small blocks of 10 cm × 5 cm × 4 cm.
How many blocks do we get? What will be the total surface area of all these blocks?
16. The dimensions of a building are 30 m × 20 m × 40 m. If the walls, floor and roof of this building are to
be repaired, the contractor asks for ` 50 per square metre. What will be the estimate of the contractor for
this work?
17. If the edge of a cube is doubled, what will be the change in its surface area?
2
18. The area of four walls of a room is 105 m . If the room is 13 m long and 4.5 m broad, find its volume.

Cylinder
Let’s consider objects like a gas cylinder, coke cans, etc. These solids B
have a curved lateral surface with congruent circular ends. Such solids
are known as right circular cylinders. A right circular cylinder has two
plane ends, also called base of the cylinder (Fig. 22.2). The two bases Axis
are circular in shape and parallel to each other.
Axis: The line segment joining the centres of the two bases is called A
the axis of the cylinder. In Fig. 22.2, AB is the axis of the cylinder. The Fig. 22.2
axis of the cylinder is perpendicular to the circular ends.
Surface area of right circular cylinder
A A
Consider a right circular cylinder of radius r and height h A
(Fig. 22.3). Each of the base is a circle of radius r. Therefore,
length of each circular edge is 2pr. h
Lateral surface area or curved surface area (CSA)
= Area of the rectangle (assuming the cylinder is cut O r 1 2pr
vertically and rolled out) A 1 A A 1
= Area of the rectangle with length ‘2pr’ and breadth ‘h’ Fig. 22.3
= 2prh sq. units
2
Base surface area = pr sq. units
Total surface area (TSA) = Curved surface area + Area of the two bases
2
= (2prh + 2pr ) sq. units = 2pr (h + r) sq. units
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