Question

. If the radius is doubled and the height is halved what is the ratio of the new volume to the original volume

Answer 1

Answer: Ratio of new volume to original volume is 2:1.

Step-by-step explanation:

Let the radius of cylinder be 'r'

Let the height of cylinder be 'h'

Original volume of cylinder will be

$V=\pi r^2h$

If radius get doubled,

New radius be '2r'

If height get halved,

New height be will be

$\frac{h}{2}$

so, Volume of cylinder becomes

$Volume=\pi (2r)^2\times \frac{h}{2}=\pi \times 4r^2\times \frac{h}{2}\\\\Volume=2\pi r^2h$

Ratio of new volume to the original volume is given by

$2\pi r^2h:\pi r^2h\\\\2:1$

Hence, Ratio of new volume to original volume is 2:1.