Page 182 - Maths Skills - 8

180 Maths

Example 3: A hall is of length 16 m, breadth 12.5 m and height 4.5 m. Calculate the number of persons that can
be accommodated in the hall, assuming 3.6 m of air is required for each person.
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Solution: Given, l = 16 m, b = 12.5 m and h = 4.5 m.

Volume of the air in the hall = Volume of the hall = l × b × h = 16 m × 12.5 m × 4.5 m = 900 m .
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Total volume of air in the hall
The number of persons accommodated in the hall =
Volume of air required for one person
900 m 3
= 3.6 m 3 = 250

So, a total of 250 persons can be accommodated in the hall.
Example 4: Find the volume of a cube whose edges are 7 cm long.

Solution: Given: a = 7 cm
\ Volume (V) = a = (7) cm = 7 × 7 × 7 cm = 343 cm .
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Example 5: A 5 cm long cube is cut into 1 cm long cubes. How many small cubes are formed?
Solution: The side of the large cube = 5 cm
\ Volume of the large cube = (5) = 125 cm 3
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The side of the small cube = 1 cm
\ Volume of the small cube = (1) = 1 cm 3
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Volume of large cube 125 cm 3
So, the number of small cubes = Volume of 1 small cube = 1 cm 3 = 125.

Example 6: The volume of a cuboidal block is 300 cm . If it is 20 cm long and 6 cm wide, find its height.
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Solution: Given: V = 300 cm , l = 20 cm and b = 6 cm
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V 300
V = l × b × h ⇒ h = = = 2.5 cm.
l × b 20 × 6
Hence, the length of the water tank is 2.5 cm.

Example 7: The rainfall on a certain day was 5 cm. How many litres of water fell on 3 hectares of a field on
that day?

Solution: Given that area of the field = 3 hectares = 3 × 10000 m 2 [ 1 hectare = 10000 m ]
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= 30000 m = 30000 × 100 dm = 3000000 dm 2 [ 1 m = 100 dm ]
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5 1
The depth of rainwater on the field = 5 cm = dm = dm.
10 2
The volume of rainwater on the field = (area of the field) × (depth of water on it)
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= 3000000 dm = 1500000 dm 3
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= 1500000 litres = 15 × 10 litres. [ 1 dm = 1 l]
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Exercise 11.3

1. Find the volume of the cube whose side is
(i) 5 cm (ii) 6.5 cm (iii) 14 cm (iv) 1.2 m