There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.

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Solution

Let the radius of the base of the cone be r m.

Height of the conical tent, h = 18 m

Area occupied by each person on the ground = 4 m²

∴ Area occupied by 25 persons on the ground = 25 × 4 m² = 100 m²

⇒ Area of the base of the cone = $π$ r² = 100 m² .....(1)

∴ Volume of the conical tent = $\frac{1}{3} π r^{2} h = \frac{1}{3} \times 100 \times 18$ = 600 m³ [Using (1)]

Thus, the volume of the tent is 600 m³.

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