Q.A vertical conical tent can accommodate 11 people. Each person requires 4 square meters of ground space and 20 cubic meters of air. Determine the height of the tent designed specifically for those 11 people.

If each person requires 4 square meters of space, then the base area of the vertical circular cone-shaped tent will be: \(4 × 11 = 44\) square meters And since each person needs 20 cubic meters of air, the volume of the tent must be: \(20 × 11 = 220\) cubic meters Let the radius of the base of the cone be \(r\) meters and the height be \(h\) meters So, base area: \(πr^2 = 44\) and volume: \(\frac{1}{3}πr^2h\) cubic meters According to the question: \(\frac{1}{3}πr^2h = 220\) ⇒ \(\frac{1}{3} × 44 × h = 220\) ⇒ \(h = \frac{220 × 3}{44} = 15\) ∴ The height of the tent is 15 meters.
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