In a right circular conical tent, 11 persons can stay. For each person, 4 sq. m space in the base and 20 cu.m. air are necessary. Determine the height of the tent put up exactly for 11 persons.
WBBSE
Class X
Mathematics
Right Circular Cone
04 Mark
2022
Base area needed for 11 person = 11 × 4 = 44 m²
Air (volume) needed for 11 person = 11 × 20 = 220 m³
For a cone:
base area = πr² = 44
⇒ r² = \frac{44}{\pi}
Volume = 220 m³
⇒ \frac{1}{3}πr²h = 220
⇒ \frac{1}{3} × π × \frac{44}{\pi} × h = 220
⇒ 44 × \frac{h}{3} = 220
⇒ h = \frac{220 \times 3}{44} = 15 m
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