The ratio of the height to the radius of a cylinder is 3:2. The volume of the cylinder is 12,936 m^3. The radius of a cone is the same as the radius of the cylinder, and the height of the cone is half the height of the cylinder. Find the volume of the cone.

1829 m³
1589 m³
1828 m³
None of these

Correct answer: None of these

Solution

For the same radius, the cone's height is half the cylinder's height, so the cone volume is \(\frac{1}{3}\pi r^2 \cdot \frac{h}{2} = \frac{1}{6}\) of the cylinder volume. Thus, cone volume = \(12936/6 = 2156\,m^3\), which is not listed. Therefore, the correct option is None of these.

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