Multiple choice

A circus tent has a cylindrical base surmounted by a conical roof. The radius of the cylindrical part is 30 m and its height is 9 m. Find the volume of air contained in the tent if the total height of the tent is 24 m. Also, find the volume of air available per person if 15 persons are seated in the tent.

  1. 39,600 m3, 2640 m3

  2. 42,360 m3, 4260 m3

  3. 39,600 m3, 4260 m3

  4. 39,600 m3, 2460 m3

  5. 38,600 m3, 2460 m3
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A Correct answer
Explanation

Volume = Volume of cylinder + Volume of cone. Cylinder: pi * 30^2 * 9 = 8100 * pi. Cone: (1/3) * pi * 30^2 * (24-9) = 4500 * pi. Total = 12600 * pi = 12600 * 3.1428... approx 39600. Per person = 39600 / 15 = 2640.

AI explanation

The height of the conical part is the total height minus the cylindrical height, which is 24 m minus 9 m to equal 15 m. Using the volume formulas, the cylindrical volume is pi*30*30*9 and the conical volume is (1/3)*pi*30*30*15, giving a combined volume of 39600 cubic m. Dividing this total volume by 15 people gives 2640 cubic m of air per person.

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