Question

The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 1500π ft2 and a radius of 15 ft.

l =
ft

Answer 1

Surface area of a right cone: S = π r l + π r^2 = π r(l + r).
Solve for l: l = S/(π r) − r.

Substitute S = 1500π and r = 15:
l = (1500π)/(π·15) − 15 = 1500/15 − 15 = 100 − 15 = 85.

Answer: l = 85 ft.