Math CentralQuandaries & Queries


Question from yash, a student:

a conical tent is to accommodate 11 people. Each person must have 4m square of space on the ground and 20m cube at air to breathe. Find the height and radius of the conical tent.


You need to know the area of a circle is $\pi \; r^2$ square meters if the radius is $r$ meters and the volume of a cone is $\pi \; r^2 h$ cubic meters if the radius of the base is $r$ meters and the cone is $h$ meters high.

If each person needs 4 square meters of space on the ground then the area of the base must be $4 \times 11 = 44$ square meters. If the area of a circle is 44 square meters what is the radius?

If each person needs 20 cubic meters of air then the cone must have a volume of at least $20 \times 11$ cubic meters. You know the radius of the base so what does the height need to be?


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