A conical tent is to accommodate 11 persons such that each person occupies 4 m2 of space on the ground.

Question:

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 breathe. The height of the cone is
(a) 14 m
(b) 15 m
(c) 16 m
(d) 20 m

Solution:

(b) 15 m

Suppose that the height of the cone is h m.

Area of the ground $=11 \times 4=44 \mathrm{~m}^{2}$

$\therefore \pi r^{2}=44$

$\Rightarrow r^{2}=\frac{44 \times 7}{22}=14$

Also, $\frac{1}{3} \pi r^{2} h=220$

$\Rightarrow \frac{1}{3} \times \frac{22}{7} \times 14 h=220$

$\Rightarrow h=\frac{220 \times 21}{22 \times 14}=15 \mathrm{~m}$

Hence, the height of the cone is 15 m.

 

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