Please help!

Question

A right circular cone is embedded inside a sphere such that the rim of the base and the vertex of the cone are on the surface of the sphere. Given that the cone has a height of 8 cm and a base radius of 4 cm, find the radius of the sphere.

Answer 1

the height of the cone goes through the center of the sphere

when the height gets to the center, this distance from the surface of the sphere to the center is the radius of the sphere

the base radius goes from the center of the circular base of the cone to the surface of the sphere

draw another radius from the surface of the sphere to the center of the sphere

this radius of the sphere which is R, the radius of the cone which is 4, and the remaining part of the height from the center of the sphere to the base of the cone which is 8-R, form a right triangle

R is the hypotenuse, and 4 and 8-R are the legs

using the Pythagorean Theorem...

R^2=4^2+(8-R)^2

R^2=16+64-16R+R^2

the two R^2's cancel each other out

0=16+64-16R

16R=80

R=80/16

R=5 cm, the radius of the sphere