Help me with this one.

Question

A cone circumscribes a sphere of radius 5 inches. If another sphere circumscribes this cone, what is the minimum surface area of this sphere circumscribing the cone that has a smaller sphere inside it?

Answer 1

Think of this in two dimensions - a circle centered at the circumcenter of an equilateral triangle.

Draw and label a diagram.

Determine the distance from the center of the circle to a vertex.

This distance is the radius of the circumscribed circle, and the circumscribed sphere