Page 285 - Start Up Mathematics_8 (Non CCE)

Volume of box
\ Number of soap cakes that can be put in the box =
Volume of 1soap cake
12 60 000, ,
= = 31,500
40

Example 9: Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of
3
the reservoir is 108 m , find the number of hours it will take to fill the reservoir. (NCERT)
3
3
Solution: Volume of reservoir = 108 m = (108 × 1,000) L = 1,08,000 L ( 1 m = 1,000 L)
Rate of pouring of water = 60 litres/minute
fi In 1 minute, volume of water filled = 60 L
\ In 1 h (i.e., 60 minutes), volume of water filled = 60 × 60 = 3,600 L
Now 3,600 L water is filled in 1 h

1
fi 1 L water is filled in h
3 600,

Ê 1 ˆ
fi 1,08,000 L water is filled in Á Ë 3 600, ¥ 108 000, , ˜ h = 30 h
¯
Hence, the reservoir will be filled in 30 hours.
Example 10: A field is 70 m long and 40 m wide. In one corner of the field, a pit which is 10 m long, 8 m
broad and 6 m deep has been dug. Soil taken out of it is evenly spread over the remaining
part of the field. Find the rise in the level of the field.
Solution: Length of the field = 70 m, Width of the field = 40 m
\ Area of the field = 70 m × 40 m = 2,800 m 2
2
Area of the pit = (10 × 8) m = 80 m 2
2
Area over which soil is spread out = (2,800 – 80) m = 2,720 m 2
3
Volume of soil dug out = (10 × 8 × 6) m = 480 m 3
70 m
Volume of soil dug out
Rise in level =
Area of over which soil is spread outt

Ê 480 ˆ Ê 480 ˆ 40 m 10 m
= Á ˜ m = Á ¥ 100 cm
˜
Ë
¯
2 720,
¯
Ë
2 720,
8 m
= 17.64 cm (approx.)
Hence, the rise in the level of the field = 17.64 cm (approx.)
Example 11: An open rectangular tank when measured from outside is 2.25 m long, 2.12 m wide and
110 cm deep. It is made up of iron which is 3.5 cm thick. Find the capacity of the tank and
the volume of iron used.
Solution: External length of tank = 2.25 m = (2.25 × 100) cm = 225 cm
External width of tank = 2.12 m = (2.12 × 100) cm = 212 cm
External depth of tank = 110 cm

\ External volume of tank = 225 cm × 212 cm × 110 cm = 52,47,000 cm 3
Internal length of tank = {225 – (3.5 × 2)} cm = (225 – 7) = 218 cm
Internal width of tank = {212 – (3.5 × 2)} cm = 212 – 7 = 205 cm

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