Volume of a solid

• Dec 7th 2006, 08:51 PM
viet
Volume of a solid
A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
• Dec 8th 2006, 03:16 AM
Soroban
Hello, viet!

I assume this is a Calculus problem . . .

Quote:

A ball of radius 15 has a round hole of radius 8 drilled through its center.
Find the volume of the resulting solid.

Code:

                |15               * * *           *:::::|:::::*         *:::::::|:::::::*       *- - - -8+ - - - -*P                 |       *        |        *   - - * - - - - + - - - - * - -       *        |        *15                 |       *        |        *         *      |      *           *    |    *               * * *                 |

The circle has equation: . $x^2 + y^2 \:=\:225\quad\Rightarrow\quad y \:=\:\pm\sqrt{225-x^2}$
The region between the circle and $y = 8$ is revolved about the x-axis.

The coordinates of point $P$ are: . $\left(\sqrt{161},\,8\right)$

The volume of revolution is: . $V \;= \; 2 \times \pi\int^{\sqrt{161}}_0\left[(225 - x^2) - 8^2\right]\,dx$