Hello,echellyluv!
I assume there is a word left out . . .
Triangle $\displaystyle ABC$ with sides $\displaystyle AB=10,\;AC=10,\;BC=12$
is rotated about the altitude to $\displaystyle BC.$
What is the volume of the cone formed?
The volume of a cone is: .$\displaystyle V \;=\;\tfrac{\pi}{3}r^2h$
Code:
A
*
/|\
/ | \
/ | \
10 / | \ 10
/ |h \
/ | \
/ | \
B * - - - * - - - * C
6 D 6
$\displaystyle AD=h$ is the altitude to side $\displaystyle BC.$
Pythagorus says: .$\displaystyle h^2 + 6^2 \:=\:10^2 \quad\Rightarrow\quad h \,=\,8$
We have: .$\displaystyle r = 6,\;h = 8$
. . Therefore . . .