Question

A textile industry runs in a shed. This shed is in the shape of a cuboid surmounted by a half-cylinder. If the base of the industry is of dimensions 14 m × 20 m and the height of the cuboidal portion is 7 m, find the volume of air that the industry can hold. Further, suppose the machinery in the industry occupies a total space of 400 m³. Then, how much space is left in the industry?

Answer 1

Given:

Height of cuboid = 7 m

Length of cuboid = 20 m

Width of cuboid = 14 m

Radius of cylinder = `14/2` = 7 m.

Height of cylinder = 20 m

volume of air inside the industry = volume of cuboid + volume of half Cylinder.

Volume of cuboid= 7 × 14 × 20

= 1960m³

volume of cylinder = `1/2 xx 22/7 xx 7 xx 7 xx 20`

= 1540m³

Thus, volume of air inside the industry

= 1960 + 1540

= 3500m³

Total space occupied by machinery = 400m³

∴ Space left in the industry = 3500 − 400

= 3100m³