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 500π ft2 and a radius of 15 ft.
l =
ft

Surface area of cone can be calculated using the following rule:
area of cone = pi (radius)^2 + pi (radius) (height)

we have the area and the radius as given and the value of pi is a constant = 22/7.

So, all we need to do is just substitute in the above equation to get the value of the height as follows:
500 pi = pi (15)^2 + pi (15)(l)    
we will divide all terms by pi
500 = (15)^2 + 15l
15l = 500 - (15)^2
15l = 275
l = 275/15 = 18.334 ft