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Standard IX

Mathematics

Total surface area of a right circular cylinder

Shanta runs a...

Question

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. (Take $π = \frac{22}{7}$ )

$1128 m^{3}$

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$1128.75 m^{3}$

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$1126 m^{3}$

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$1121 m^{3}$

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Solution

The correct option is B
$1128.75 m^{3}$

Now, the length, breadth and height of the cuboid are 15 m, 7 m and 8 m, respectively.

Also, the diameter of the half cylinder is 7 m and its height is 15 m.

So, the required volume = volume of the cuboid + $\frac{1}{2}$ volume of the cylinder

= $[15 \times 7 \times 8 + \frac{1}{2} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 15] m^{3} = 1128.75 m^{3}$

$= 1128.75 m^{3}$

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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. (Take π=227)

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