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(A) The volume of a cylinder is given by the formula $V = \pi r^2 h$,where $r$ is the radius and $h$ is the height.Let the initial radius be $r$ and t

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halved

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(A) The volume of a cylinder is given by the formula $V = \pi r^2 h$,where $r$ is the radius and $h$ is the height.Let the initial radius be $r$ and the initial height be $h$. The initial volume is $V_1 = \pi r^2 h$.According to the problem,the new radius $r' = \frac{r}{2}$ and the new height $h' = 2h$.The new volume $V_2$ is calculated as:$V_2 = \pi (r')^2 (h')$$V_2 = \pi (\frac{r}{2})^2 (2h)$$V_2 = \pi (\frac{r^2}{4}) (2h)$$V_2 = \frac{2}{4} \pi r^2 h$$V_2 = \frac{1}{2} \pi r^2 h$Since $V_1 = \pi r^2 h$,we have $V_2 = \frac{1}{2} V_1$.Therefore,the volume is halved.

In a cylinder,if the radius is halved and the height is doubled,the volume will be

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