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A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath. Find the height of the cone.

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10 m

20 m

15 m

25 m

answer is C.

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Detailed Solution

Given,
A conical tent is to accommodate 11 persons
Each person must have 4 sq. meters
Area of base occupied by the persons,

A = 11 \times 4

A = 44 m^{2}

Area of base, If radius =r,

A = π r^{2}

π r^{2} = 44

So, volume of the cone occupied by the persons,

V = 11 \times 20

V = 220 m^{3}

Now volume of the cone,

V = \frac{1}{3} π r^{2} h

\frac{1}{3} π r^{2} h = 220 m^{3}

The ratio of the volume to the area of cone is,

\Rightarrow \frac{V}{A}

\Rightarrow \frac{\frac{1}{3} π r^{2} h}{π r^{2}} = \frac{220}{44}

\Rightarrow \frac{h}{3} = \frac{220}{44}

\Rightarrow h = 15 m

Thus, the height of the cone = 15 m.
Correct option is 3.

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