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. The height of the cone is :
Options:
A . 13 m
B . 14 m
C . 15 m
D . 16 m
Answer: Option C Let the radius of base = r and height = h Required floor area : = (4 × 11) m2 = 44 m2 Required volume : = (20 × 11) m3 = 220 m3 So, $$\eqalign{ & \frac{1}{3}\pi {r^2}h = 220 \cr & \Rightarrow \frac{1}{3} \times 44 \times h = 220 \cr & \Rightarrow h = \frac{{220 \times 3}}{{44}} \cr & \Rightarrow h = 15\,m \cr} $$
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