Krishna runs an industry in a shed, which is in the shape of a cuboid surmounted by a half cylinder. If the base of the shed is of dimension 5 m × 15 m and the height of the cuboidal portion is 7 m, find the volume of the air that the shed can hold. [Use π=22/7]

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Solution

Step 1:
Find the volume of the cuboid and half cylinder.

Volume of cuboid $= 5 \times 15 \times \times 7 = 525 m^{3}$
Volume of half cylinder $= \frac{1}{2} π r^{2} h$
$= \frac{1}{2} \times \frac{22}{7} \times (\frac{5}{2})^{2} \times 15$
$= 147.32 m^{3}$

Step 2:
Total Volume = Volume of cuboid + Volume of half cylinder.
$= 525 + 147.32 m^{3}$
$= 672.32 m^{3}$
The shed can store $672.32 m^{3}$ of air inside it.

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