Shanta runs an industry in a shed that was in the shape of a cuboid surmounted by half-cylinder. If the base of the shed is $7 m \times 15 m$ and height of the cuboidal portion is $8 m$ , find the volume of the air that the shed can hold. If the industry requires machinery which would occupy a total space of $300 m^{3}$ , and there are $20$ workers each of whom would occupy $0.08 m^{3}$ space on an average, how much air would be in the shed when it is working. $(T a k e π = \frac{22}{7})$

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Solution

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 $= 15 m$ ; breadth $= 7 m$ and height $= 8 m$
Volume of cuboidal part $= 15 \times 7 \times 8 m^{2} = 840 m^{3}$

Clearly
Radius $= r = \frac{7}{2} m$

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

Volume of half cylinder
$= \frac{1}{2} π r^{2} h = \frac{1}{2} \times \frac{22}{7} \times {(\frac{7}{2})}^{2} \times 15 m^{3} = 288.75 m^{3}$

Volume of air inside the shed when there is no people or machinary
$= (840 + 288.75) m^{3} = 1128.75 m^{3}$

Total space occupied by 20 workers $= 20 \times 0.08 m^{3} = 1.6 m^{3}$

Total space occupied by the machinery $= 300 m^{3}$

Volume of the air inside the shed when there are machine and workers inside it
$= (1128.75 - 1.6 - 300) m^{3} = 827.15 m^{3}$

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Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see Fig.). If the base of the shed is of dimension 7 m × 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 $m^{3}$ , and there are 20 workers, each of whom occupy about 0.08 $m^{3}$ space on an average. Then, how much air is in the shed (in $m^{3}$ )? (Take $π = \frac{22}{7}$ )

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