Question

A sphere of radius `15` inches rest on a circular hole of diameter `10` inches cut into a board. How far does the sphere extend below the surface of the board?

Answer 1

`15 - 10sqrt(2) ~~ 0.858` inches

Explanation:

In this diagram:

`a = sqrt(15^2 - 5^2) = sqrt(225-25) = sqrt(200) = 10sqrt(2)`

So the sphere extends `15 - a = 15 - 10sqrt(2)` inches below the upper surface of the board.