Shanta runs an industry in a shed which is in the shape of a cubeoid surmounted by half cylinder - Maths - Surface Areas and Volumes

Question

Shanta runs an industry in a shed which is in the shape of a
cubeoid surmounted by half cylinder If the base of the shed is of
demension 7m x 15m , 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 accupies a total space of 300m3,
and there are 20 workers each of whom ocupy about 0 08 m
3 space on a average Then how much air is in the
shed?

Ankush Jain · Accepted Answer

The volume of air inside the shed (when there are no people or machinery) is given by the volume of air inside the cuboid and inside the half cylinder taken together. Given, the length, breadth and height of the cuboid are 15m, 7m and 8m respectively.

Also the diameter of half cylinder = 7 m

∴ radius of half cylinder $= \frac{7}{2} = 3.5 m$

and the height of half cylinder = 15 m

so, the volume of air inside the shed = volume of cuboid + $\frac{1}{2}$ (volume of cylinder)

$= [15 \times 7 \times 8 + \frac{1}{2} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 15] m^{3}$

= 1128.75 m³

The total space occupied by the machinery = 300 m³ and the total space occupied by the workers = 20 × 0.08 m³ = 1.6 m^3.

Therefore, the volume of air, when there are machinery and workers = (1128.75) – (300 + 1.6) = 827.15 m³

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