The formula for the slant height of a cone is t equals StartFraction S minus pi r squared Over pi EndFraction. , 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 500π ft2 and a radius of 15 ft.

l = _____ ft

1 answer

First, we need to know the formula for the surface area of a cone:

S = πr^2 + πrl

Given that S = 500π ft^2 and r = 15 ft, we can substitute these values into the formula:

500π = π(15)^2 + π(15)l
500π = 225π + 15πl
500 = 225 + 15l
275 = 15l
l = 18.33 ft

Therefore, the slant height of the cone is 18.33 ft.