The radius of a cylinder is made twice as lar | vedclass

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(A) Let the original radius be $r$ and the original height be $h$. The original volume $V$ is given by $V = \pi r^2 h$.If the new radius is $R = 2r$ a

Vedclass · Accepted Answer

$1/4$ of original

Vedclass · Answer

(A) Let the original radius be $r$ and the original height be $h$. The original volume $V$ is given by $V = \pi r^2 h$.If the new radius is $R = 2r$ and the new height is $H$,the new volume $V'$ must be equal to $V$.So,$V' = \pi R^2 H = \pi (2r)^2 H = \pi (4r^2) H = 4 \pi r^2 H$.Since $V' = V$,we have $4 \pi r^2 H = \pi r^2 h$.Dividing both sides by $\pi r^2$,we get $4H = h$,which implies $H = \frac{1}{4} h$.Therefore,the height should be $\frac{1}{4}$ of the original height.

The radius of a cylinder is made twice as large. How should the height be changed so that its volume remains unchanged?

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