The radius of the cylinder is made twice as l | vedclass

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(B) The volume of a cylinder is given by $V = \pi r^2 h$.Let the original radius be $r$ and the original height be $h$. The original volume is $V_1 =

Vedclass · Accepted Answer

$1/4 	imes$ original height

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(B) The volume of a cylinder is given by $V = \pi r^2 h$.Let the original radius be $r$ and the original height be $h$. The original volume is $V_1 = \pi r^2 h$.If the new radius $r' = 2r$,let the new height be $h'$.For the volume to remain the same,$V_2 = V_1$,so $\pi (r')^2 h' = \pi r^2 h$.Substituting $r' = 2r$: $\pi (2r)^2 h' = \pi r^2 h$.$\pi (4r^2) h' = \pi r^2 h$.$4 h' = h$.Therefore,$h' = \frac{1}{4} h$.The height should be changed to $\frac{1}{4}$ of the original height.

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

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