A conical tent is to accommodate 11 persons such that each person occupies 4 m² of space on the ground. They have 220 m³ of air to breath in the tent. The height of the cone is

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16 m

15 m

14 m

20 m

answer is B.

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Detailed Solution

Persons are there each person occupies 4 m² on the ground

$\begin{array}{l} A r e a o f g r o u n d = 11 \times 4 \\ \begin{array}{l} π r^{2} = 11 \times 4 & r^{2} = 14 \\ \frac{22}{7} r^{2} = 44 \end{array} \end{array}$

$\begin{array}{l} V_{c o n e} = 220 \\ \frac{π r^{2} h}{3} = 220 \\ \frac{22}{3 \times 7} \times 14 \times h = 220 \\ h = 15 m \end{array}$

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