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Question

A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 m3. The maximum volume available to place machinery in the factory is .

(Take π=227)

A
5805 m3
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B
8885 m3
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C
5880 m3
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Solution

The correct option is A 5805 m3

The factory is a combination of a cuboid of dimensions 40m x 14m x 5m and half a cylinder of radius 7m and height 40m.
We know that volume of cuboid = lbh
and volume of cylinder = πr2h

We have, volume of the factory
=lbh+12πr2h
= 40×14×5+12×π×(7)2×40
= 2800 + 3080
= 5880m3

Volume occupied by people = 150×0.5=75 m3

Maximum volume permissible for machinery = 5880 - 75 = 5805m3


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