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 $m^{3}$ . Find the maximum volume available to place machinery in the factory in $m^{3}$ . (Take $π = \frac{22}{7}$ )

5805

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Solution

The correct option is A 5805
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 = $π r^{2} h$

We have, volume of the factory
$= l b h + \frac{1}{2} π r^{2} h$
= $40 \times 14 \times 5 + \frac{1}{2} \times π \times (7)^{2} \times 40$
= 2800 + 3080
= 5880 $m^{3}$

Volume occupied by people = $150 \times 0.5 = 75 m^{3}$

Maximum volume permissible for machinery = 5880 - 75 = 5805 $m^{3}$

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