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A conical tent is to accommodate 11 persons. Each person must have 4 m2 of the space on the ground and 20 m3 of air to breathe. Find the height of the cone.

Asked by Topperlearning User 10th April 2014, 8:54 AM
Answered by Expert
Answer:

Let the radius of the conical tent be 'r' m and height be 'h' m.

Space on the ground required by each person = 4 m2

Area of base = 11 4 = 44 m2

Air required by each person to breathe = 20 m3

Volume of cone = 11 20 = 220 m3

Area of the base of conical tent =

Volume of cone = 220

1 third πr squared straight h equals 220
rightwards double arrow 1 third cross times 22 over 7 cross times open parentheses square root of 14 close parentheses squared cross times straight h equals 220
rightwards double arrow straight h equals fraction numerator 220 cross times 3 cross times 7 over denominator 22 cross times 14 end fraction equals 15 space straight m

Thus, height of the cone is 15 m.

Answered by Expert 10th April 2014, 10:54 AM
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