# Volume of a solid

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