Hello, stones44!

A cone with a 10-inch diameter is 12 inches tall.

a. Find the radius of the largest sphere that can be inscribed in the cone.

b. The volume of this sphere is what percentage of the volume of the cone? Code:

- : - - - 5 - - - D - - - 5 - - - :
C * - - - - - - - * * * - - - - - - - * B
: \ * | * /
: \ * | * /
: \ * |r * /
: \ | /
: \ * | * /
: \ * O* * /
: \* | \ */
12 \ | \r /
: * | \ *
: * | *E
: \* | */
: \ * * * /
: \ | /
: \ | /
: \ | /
: \ | /
: \|/
- *
A

We have: .

. . From Pythagorus: .

The center of the sphere is

Radii

. . Hence: .

We have similar right triangles: .

So we have: .

Therefore: .

.