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Resources Question 1 of 14 Q
A cone and a cylinder have the same height and the same radius. If the volume of the cylinder is $162 \mathrm{~cm}^{3}$, what is the volume of the cone?
$486 \mathrm{~cm}^{3}$
$81 \mathrm{~cm}^{3}$
$324 \mathrm{~cm}^{3}$
$54 \mathrm{~cm}^{3}$

Step 1 ：Given the volume of the cylinder is \(162 \mathrm{~cm}^{3}\), and the cone and cylinder have the same height and radius.

Step 2 ：The formula for the volume of a cylinder is \(V_{cylinder} = \pi r^2 h\), and the formula for the volume of a cone is \(V_{cone} = \frac{1}{3} \pi r^2 h\).

Step 3 ：Since the cone and cylinder have the same height and radius, we can write the volume of the cone as \(V_{cone} = \frac{1}{3} V_{cylinder}\).

Step 4 ：Substitute the given volume of the cylinder: \(V_{cone} = \frac{1}{3} (162)\).

Step 5 ：Calculate the volume of the cone: \(V_{cone} = 54\).

Step 6 ：\(\boxed{54 \mathrm{~cm}^{3}}\) is the volume of the cone.