# Math Help - volume of a cone

1. ## 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?

2. 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 . . .