Question

The radius of a cylinder is doubled due to which the volume of the new cylinder also gets doubled. The height of the new cylinder is what percentage of the old cylinder?

• A. 200%
• B. 100%
• C. 25%
• D. 50%

Answer 1

Answer:

D. 50%

Volume of a cylinder:

$V = \pi r^2 h$

Let the original radius = ( r ) and height = ( h )

Original volume:
$V = \pi r^2 h$

Radius is doubled ⇒ New radius = ( 2r )

New volume:
$V' = \pi (2r)^2 h'$
$= \pi \cdot 4r^2 \cdot h'$
$= 4\pi r^2 h'$

Given that the new volume is double the old volume:

$4\pi r^2 h' = 2(\pi r^2 h)$
$Cancel ( \pi r^2 ):$

$4h' = 2h$
$h' = \frac{2h}{4}$
$h' = \frac{h}{2}$

So, the new height is half of the old height.
$\frac{h'}{h} \times 100 = \frac{1}{2} \times 100$ = 50
The height of the new cylinder is 50% of the old cylinder.