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.
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