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 $m^3$. The maximum volume available to place machinery in the factory is .

(Take $\pi =\frac{22}{7}$)

• A. 5805 $m^3$
• B. 8885 $m^3$
• C. 5880 $m^3$

Answer 1

The correct option is A 5805 $m^3$

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 = $\pi r^{2}h$

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

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

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