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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?

 Feb 25, 2021
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The radius of the cone is 1/2 the triangle's side length, so 6 centimeters. The height is 6sqrt(3) centimeters.

 

\(V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \cdot (6^2)(6\sqrt{3}) = \boxed{72 \sqrt{3} \pi}\)

 Feb 25, 2021

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