In a tall circular conical tent, 11 people can stay. Each person requires 4 square meters of floor space and 20 cubic meters of air. Determine the height of the tent designed specifically for these 11 people.

Q.In a tall circular conical tent, 11 people can stay. Each person requires 4 square meters of floor space and 20 cubic meters of air. Determine the height of the tent designed specifically for these 11 people.

If each person requires 4 square meters of space, then the floor area of the tall circular conical tent is: \(4 × 11 = 44\) square meters. And the volume of the cone must be: \(20 × 11 = 220\) cubic meters. Let the base radius of the cone be \(r\) meters, and the height be \(h\) meters. ∴ Floor area, \(πr^2 = 44\) And volume, \(= \cfrac{1}{3} πr^2 h\) cubic meters. According to the problem, \(\cfrac{1}{3} πr^2 h = 220\) i.e., \(\cfrac{1}{3} × 44 × h = 220\) ∴ \(h = \cfrac{220 × 3}{44} = 15\) ∴ The height of the tent is 15 meters.