Hello, dannyshox!

A hole of diameter is bored through the centre of a sphere of radius

Show that the remaining volume is:Code:| * * * *:::::|:::::* - * - - - + - - - * - y = a/2 *| | |* | | | * | | | * ----*-+-------+-------+-*---- * | | | *a | | | *| | |* * - - - | - - - * * | * * * * |

The equation of the circle is: .

The equation of the horizontal line is: .

Revolve the shaded region about the -axis.

That is the desired volume.

The graphs intersect for: .

. . Substitute [2] into [1]: .

Formula: .

Due to symmetry: . .

Got it?