Maxima and Minima

Question

A sphere is inscribed in a right circular cone. Find the dimensions of the cone if the diameter of the sphere is 16cm.

Answer 1

You have left out something....

We can look at this problem in 2 dimensions---a slice down the center shows us a circle inside of a triangle.

There are an infinite number of shapes for the triangle that encloses a given circle.

Did you maybe mean that we should find the minimum or maximum of a parameter??

Answer 2

Since the sphere is tangent to the base of the cone, the height of the cone will be 8 + the distance from the center of the sphere to the apex of the cone. This distance (diagonal of a square ) is seen to be 8 sqrt(2). So the height of the cone is 8( 1 + sqrt(2)).

Since it is a right circular cone, the radius of the base is the same: 8(1 + sqrt(2))

Answer 3

The formula for cones and pyramids is bh/3.

Sphere dia=16cm

circle area= r^2pi

256pi=804.248sq/cm

On the other hand; how deep does the sphere sit? What angle is the cone?