Sorry, I misread the question.
Lateral surface area = 48π = πrL
48π = π(8)L
6 = L
There is a problem here. The slant height is a hypotenuse of a triangle consisting of the altitude and the radius. The slant height has to be greater than the measure of both the radius and the altitude, but 6 < 8. So, this cannot exist, after all the flat base area is 64π, how can it be covered by a cone of smaller area?
IF the slant height was 8, then the radius would be 6, and all would be well.
