A tent is being designed in the shape of a cone with a slant height of 18.5 feet and a diameter of 20 feet.

Question

Approximately how much material is needed to cover the lateral area of the tent without any overlap? Round your answer to the nearest tenth

Answer 1

The formula for the lateral area of the cone is pi r l where r is the radius of the cone and l and the length of the slant. Thus the answer is pi (18.5)(10) = 581 ft^2.

For some insight as to why this formula holds note that when you unroll it (google images for an example) you get a circle of radius l but you're only taking a proportion of it. So the entire area is pi l^2 but since you're only taking (r/l) proportion of that circle your area is pi l^2 (r/l) = pi r l.

Answer 2

A_L = πrs, s means slant height.