Question

What is the effect on the volume of a cylinder if the radius is doubled while the height is halved?A. The volume is halved.B. The volume remains the same.C. The volume is multiplied by 4.D. The volume is doubled.

Answer 1

Given that

There is a cylinder and we have to find the change in its volume if the radius is doubled and the height is halved.

Explanation -

Let the Initial radius be r and the height be h. Then the initial volume will be

`v=\pi* r^2* h-----------(i)`

Now applying the given changes,

new radius = 2 x r

new height = h/2

Then the new volume will be V,

`\begin{gathered} V=\pi*(2r)^2*(h)/(2) \\ \\ V=\pi*4r^2*(h)/(2) \\ \\ V=2*\pi* r^2* h \\ \\ On\text{ substituting v = }\pi* r^2* h \\ \\ V=2* v \end{gathered}`

Hence volume will be doubled. And option D is correct.

Final answer -

Therefore the final answer is OPTION D.