Question

X and Y are two cylinders of the same height. The base of X has diameter that is half the diameter of the base of Y. If the height of X is doubled, the volume of X becomes:

• A. Equal to the volume of Y
• B. Double the volume of Y
• C. Half the volume of Y
• D. Greater than the volume of Y
• E. None of these

Answer 1

The correct option is C

Half the volume of Y

Let the height of X and Y be `h', and their radii be r and 2r respectively.
Then, volume of X = $\pi$r${}^2$h and volume of Y = $\pi$ (2r)${}^2$, h = 4$\pi$r${}^2$h
New height of X = 2h
So, new volume of X = $\pi$r${}^2$(2h) = 2$\pi$r${}^2$h=$\frac{1}{2}\left(4{\pi }^{2}h\right)=\frac{1}{2}volumeofY$