Page 240 - ICSE Math 8

2. Find the volume of a cube whose side is:
(a) 6.3 cm (b) 7.2 dm (c) 5 m
3. A water tank is 1.5 m long, 1.3 m wide and 0.5 m deep. How many litres of water can it hold?

4. What will happen to the volume of a cube, if each of its edges is halved?
5. A swimming pool is 200 m long and 120 m wide. 36 litres of water is pumped into it. Given the
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1 m = 1000 L, find the rise in level of water.
6. A cuboid has dimensions 25 dm × 15 dm × 8 dm. How much does its volume differ from that of a cube
with an edge of 16 dm?
7. The dimensions of a cistern are 2 m 75 cm × 1 m 90 cm × 1 m 40 cm. How many litres of water can this
cistern hold if we fill it completely?
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8. The volume of a cuboidal box is 250 cm . If its length is 20 cm and height is 5 cm, find its breadth.
9. How many cubes of edge 0.5 cm are required to make a cube of side 3 cm?
10. A cuboidal shape gold biscuit is of dimensions 8 cm × 5 cm × 2 cm. From this gold biscuit, small lockets
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each of volume 2.5 cm are made. How many such lockets can be made from this gold biscuit?
11. Two cubes are such that the length of the side of cube I is twice the length of the side of cube II. Find
the ratio of the volume of cube I to that of cube II.
12. How many boxes of alarm clocks each of size 5 cm × 10 cm × 10 cm can be packed into a box of size
1 3
1 m × m × m?
2 4
13. Three cubes having edges 18 cm, 24 cm and 30 cm respectively are melted to make a new cube. Find the
edge of the new cube so formed.

14. The outer dimensions of a jewellery box made of wood are 20 cm × 16 cm × 8 cm. The thickness of the
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wood is 1 cm. Find the total cost of wood required to make the box, if 1 cm of wood costs ` 2.50.

Surface Area of Solids
In this section, we will try to understand the concept of surface area of a cube and a cuboid.

Surface area of a cuboid

A cuboid consists of six rectangular faces. So, its surface area is equal to the sum of the areas of its six
rectangular faces.

Let there be a cuboid of length l cm, breadth b cm and height h cm (Fig. 22.1).
(i) Area of face ABFG = Area of face DCEH = l × b cm 2
(ii) Area of face ADHG = Area of face BCEF = b × h cm 2
(iii) Area of face ABCD = Area of face HEFG = l × h cm 2 G
Total Surface Area (TSA) of the cuboid l F

= Sum of the areas of its six faces A B
= 2(lb) + 2(bh) + 2(hl) = 2(lb + bh + hl) cm 2
b H E
Length of the diagonal (AE) = l + 2 b + 2 h cm
2
D l C
Now consider a room of length (l), breadth (b) and height (h). A
room is also a cuboid. So, the surface area of the four walls [also Fig. 22.1
called the lateral surface area (LSA)] = 2(lh) +2(bh)
\ LSA = 2h(l + b) sq. unit = 2 × height × (length + breadth) sq. unit
= (Perimeter × Height) sq. unit

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