Page 242 - ICSE Math 8

Example 13: A suitcase of measurement 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth.
How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Solution: Length (l) = 80 cm = 0.8 m, breadth (b) = 48 cm = 0.48 m, height (h) = 24 cm = 0.24 m
\ Total surface area of suitcase = 2(lb + bh + hl)
= 2 (0.8 × 0.48 + 0.48 × 0.24 + 0.24 × 0.8) m 2
2
2
= 2 (0.384 + 0.1152 + 0.192) m = 2 (0.6912) m = 1.3824 m 2
Width of cloth = 96 cm = 0.96 m
1 3824.
\ Length of cloth required to cover 1 suitcase = = 1.44 m
096.
Hence, the length of cloth required to cover 100 suit cases = 1.44 m × 100 = 144 m
Example 14: The ratio of surface areas of two cubes is 1 : 9. Find the ratio of their volumes.

Solution: Let the surface area of first cube with edge x be A and the surface area of second cube with
1
1
edge x be A . Let V and V be their respective volumes.
1
2
2
2
A 1 6x 2 1
2
Then, 1 = fi 1 = {  Surface area of cube = 6 × (edge) }
A 2 9 6x 2 2 9
x 2 1 x 1
fi 1 = fi 1 =
x 2 2 9 x 2 3
V x 3 Ê x ˆ 3 Ê 1ˆ 3 1
Now, 1 = 1 = Á 1 ˜ = Á ˜ =
V 2 x 2 3 Ë x ¯ Ë 3¯ 27
2
\ V : V = 1 : 27
1
2
Hence, their volumes are in the ratio 1 : 27.
Example 15: The dimensions of an encyclopedia are 24 cm × 12 cm × 6 cm. It is to be covered with a plastic
2
sheet. If each encyclopedia requires 170 cm of extra sheet for folding, how much plastic sheet
is required to wrap 50 such encyclopedias?
Solution: The encyclopedia is to be covered by a plastic sheet only on b = 12 cm
three faces, i.e., top, bottom and spine (the bound side).
Area of top = l × b = 24 cm × 12 m = 288 cm 2

Area of bottom = l × b = 24 cm × 12 cm = 288 cm 2 l = 24 cm
Area of spine = l × h = 24 cm × 6 cm = 144 cm 2

Area of extra sheet required for folding = 170 cm 2
6 cm
2
Area of plastic sheet required for 1 encyclopedia = (288 + 288 + 144 + 170) cm = 890 cm 2
2
\ Area of plastic sheet required for 50 such encyclopedias = (50 × 890) cm = 44,500 cm 2

EXERCISE 22.2

1. Find the total surface area and lateral surface area of a cuboid with length = 3.5 m, breadth = 32 dm and
height = 260 cm.
2. Find the length of the diagonal of a cuboid with length = 10 cm, breadth = 8 cm and height = 4 cm.
3. Find the total surface area, lateral surface area and the length of the diagonal of a cube whose edge is:
(a) 4.5 cm (b) 3.2 m (c) 12 dm (d) 1 dm 5 cm
4. Find the surface area of a cube whose volume is:
3
3
3
(a) 512 m (b) 64 dm (c) 125 cm (d) 216 m 3
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