Question

6. Shanta runs an industry in a shed which
is in the shape of a cuboid surmounted
by a half cylinder (see the given figure).
If the base of the shed is of dimension
7 m x 15 m, and the height of the cuboidal
portion is 8 m, find the volume of air that
the shed can hold. Further, suppose the
machinery in the shed occupies a total
space of 300 m' and there are 20 workers.
each of whom occupy about 0.08 m space
on an average. Then, how much air is in
22
the shed?​

Answer 1

Answer:

Clearly, the volume of air inside the shed (when there is no people or machinary) is equal to the volume of air inside the cuboid and inside the half-cylinder taken together

For cuboidal part, we have

Length =15m; breadth =7m and height =8m

Volume of cuboidal part =15×7×8m2 =840m3

Clearly ,

radius = r = 7/2 m

Height (length) of half-cylinder=h= Length of cuboid=15m

Volume of half cylinder

$\frac{1}{2} \pi {r}^{2} h$

$= \frac{1}{2} \times \frac{22}{7} \times ( { \frac{7}{2} })^{2} \times 15 {m}^{3}$

=288.75m 3

Volume of air inside the shed when there is no people or machinary

=(840+288.75)m 3

=1128.75m3

Total space occupied by 20 workers =20×0.08m3

=1.6m 3

Total space occupied by the machinery =300m3