Question

A sphere intersects a plane that is 6 units away from its center; the intersection is a circle of radius 8. What is the radius of the sphere?

Answer 1

10

Explanation:

Consider the triangle consisting of the segment from the center of the sphere to the center of the circle, a radius of the circle, and the radius of the sphere to the other end of the radius of the circle. The given leg dimensions of that right triangle are 6 and 8, so the Pythagorean theorem tells you the hypotenuse (radius of the sphere) is ...

√(6²+8²) = √(36+64) = √100 = 10

The radius of the sphere is 10 units.

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You may recognize this as a 3-4-5 right triangle scaled by a factor of 2.