A conical tent has to accommodate 75 persons. Each person must have 10 m2 of…

Concept

For any cone, Volume = (1/3) x base area x height. Because both the total base area and the total volume are already known as combined totals for all persons, the height can be found directly from this relation without separately finding the radius or using pi.

Application

1. Total ground (base) area required = 75 persons x 10 sq m per person = 750 sq m. This is the base area of the conical tent.

2. Total air volume required = 75 persons x 95 cubic m per person = 7125 cubic m. This is the volume of the cone.

3. Apply the cone volume formula: Volume = (1/3) x base area x height, so 7125 = (1/3) x 750 x height.

4. Solve for height: height = (3 x 7125) / 750 = 21375 / 750 = 28.5 m.

Cross-check

If the tent were shaped like a cylinder with the same base area, its height would simply be volume / base area = 7125 / 750 = 9.5 m. A cone's volume is exactly one-third of a cylinder sharing the same base and height, so the cone's actual height must be three times this cylinder-equivalent value: 3 x 9.5 m = 28.5 m, confirming the result.

The height of the tent is approximately 28.5 m.