Consider the right circular cone shown. If the radius of the circular base remains the same

Question

and the height varies, what are the minimum surface area and minimum volume the cone
can have?

Answer 1

No figure is shown. As I understand your description of the problem, the minimum area and volume would be obtained as the height approaches zero.

The volume would then be zero. The surface area (including base) would then approach 2 pi r^2.