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Math Help - volume of a cone

  1. #1
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    Question volume of a cone

    triangle ABC with sides AB=10, AC=10, and BC=12 is rotated about the altitude BC. what is the volume of the cone formed?
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  2. #2
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    Hello,echellyluv!

    I assume there is a word left out . . .


    Triangle ABC with sides AB=10,\;AC=10,\;BC=12
    is rotated about the altitude to BC.
    What is the volume of the cone formed?

    The volume of a cone is: . V \;=\;\tfrac{\pi}{3}r^2h

    Code:
                  A
                  *
                 /|\
                / | \
               /  |  \
           10 /   |   \ 10
             /    |h   \
            /     |     \
           /      |      \
        B * - - - * - - - * C
              6   D   6

    AD=h is the altitude to side BC.

    Pythagorus says: . h^2 + 6^2 \:=\:10^2 \quad\Rightarrow\quad h \,=\,8


    We have: . r = 6,\;h = 8

    . . Therefore . . .

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