The radius of the base of a solid cylinder is | vedclass

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(C) The volume of a cylinder is given by the formula $V_{	ext{cylinder}} = \pi r^2 h$,where $r$ is the radius and $h$ is the height.Given,$h = 3 	ex

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$9$

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(C) The volume of a cylinder is given by the formula $V_{	ext{cylinder}} = \pi r^2 h$,where $r$ is the radius and $h$ is the height.Given,$h = 3 	ext{ cm}$,so $V_{	ext{cylinder}} = \pi r^2 (3) = 3 \pi r^2 	ext{ cm}^3$.The volume of a cone is given by the formula $V_{	ext{cone}} = \frac{1}{3} \pi r^2 H$,where $H$ is the height of the cone.Since the cylinder is recast into a cone of the same radius,their volumes must be equal.Therefore,$3 \pi r^2 = \frac{1}{3} \pi r^2 H$.Dividing both sides by $\pi r^2$,we get $3 = \frac{1}{3} H$.Multiplying by $3$,we find $H = 9 	ext{ cm}$.

The radius of the base of a solid cylinder is $r \text{ cm}$ and its height is $3 \text{ cm}$. It is recast into a cone of the same radius. The height of the cone will be (in $\text{cm}$):

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