+205 An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?
+1224 The radius of the cone is 1/2 the triangle's side length, so 6 centimeters. The height is 6sqrt(3) centimeters.
\(V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \cdot (6^2)(6\sqrt{3}) = \boxed{72 \sqrt{3} \pi}\)
