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Math Help - Volume of a solid

  1. #1
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    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.
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  2. #2
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    Hello, viet!

    I assume this is a Calculus problem . . .


    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

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