Question

A factory is designed as shown in the figure. If there are 150 people working in the factory in which each of them occupy a space of 0.5 $m^3$ and are in constant motion. Find the maximum volume available to place machinery in the factory. (Take $\pi =\frac{22}{7}$)

• A. 5880m³
• B. 8960m³
• C. 8885m³
• D. 5805m³

Answer 1

The correct option is D

5805m³

The factory can be thought of as a combination of cuboid of dimensions 40m x 14m x 5m and half a cylinder of radius 7m and height 40m.

Volume of the factory $=lbh+\frac{1}{2}\pi r^{2}h$

= $40\times 14\times 5+\frac{1}{2}\pi (7{)}^2\times 40$.

= 5880$m^3$

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

Maximum volume permissible for machinery = 5805$m^3$. The people being in constant motion does not affect the volume.