How do I find the radius of a right cone with a slant of 22 and surface area of 168pi m^2?

Answer 1

You didn't say if the surface area included the base.

If it does:
πr^2 + πrs = 168π
divide by π
r^2 + 22r - 168 = 0
completing the square
r^2 + 22r + 121 = 168 + 121 = 289
(r+11)^2 = √289
r+11 = 17
r = 6

If you did not include the base,

πrs = 168π
22r = 168
r = 168/22 = 84/11