Question : A conical tent has to accommodate 25 persons. Each person must have 4 m2 of space on the ground and 80 m3 of air to breathe. Find the height of the tent.
Option 1: 60 m
Option 2: 50 m
Option 3: 40 m
Option 4: 45 m
Correct Answer: 60 m
Solution :
Given: A conical tent has to accommodate 25 persons.
Each person must have 4 m
2
of space on the ground and 80 m
3
of air to breathe.
⇒ The total base area = 4 × 25 = $\pi r^2$ = 100 m
2
The volume of the cone = $\frac{1}{3}\pi r^2h$ where $r$ and $h$ are radius and height, respectively.
The volume of the air required = 25 × 80 = 2000 m
3
.
Let the cone's height be $h$ m.
According to the question,
$\frac{1}{3}\times 100\times h=2000$
⇒ $h=\frac{2000\times 3}{100}=60$ m
Hence, the correct answer is 60 m.
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