Near the cone, the base radius of which is 4, a sphere with a radius of 5 is described, find the height of the cone.

Let’s construct the radius of the sphere OA.

In a right-angled triangle AOO1, we define, according to the Pythagorean theorem, the length of the leg OO1.

OO1 ^ 2 = AO ^ 2 – AO1 ^ 2 = 25 – 16 = 9.

OO1 = 3 cm.

Then the height of the cone is equal to: BO1 = BO + OO1 = 5 + 3 = 8 cm.

Since the condition does not indicate the location of the base of the cone relative to the center of the sphere, the height of the cone can be: AO1 = AO – OO1 = 5 – 3 = 2 cm.

Answer: The height of the cone is 8 cm or 2 cm.