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(B) The volume of a solid cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h_{cone}$.The volume of a solid cylinder is given by $V_{cylinder} = \pi r^

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$15$

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(B) The volume of a solid cone is given by $V_{cone} = \frac{1}{3} \pi r^2 h_{cone}$.The volume of a solid cylinder is given by $V_{cylinder} = \pi r^2 h_{cylinder}$.Since the material is converted from the cone to the cylinder,their volumes are equal: $V_{cone} = V_{cylinder}$.Therefore,$\frac{1}{3} \pi r^2 h_{cone} = \pi r^2 h_{cylinder}$.Given that the radii are equal,we can cancel $\pi r^2$ from both sides:$\frac{1}{3} h_{cone} = h_{cylinder}$.Given $h_{cylinder} = 5\,cm$,we have $\frac{1}{3} h_{cone} = 5\,cm$.Thus,$h_{cone} = 3 	imes 5\,cm = 15\,cm$.

The material of a solid cone is converted into the shape of a solid cylinder of equal radius. If the height of the cylinder is $5\,cm$,then what is the height of the cone? (in $cm$)

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