# If the radius of a cylinder is doubled and its height is quartered, what will be the percebt increase in its volume?

May 15, 2018

There will not be percentage increase when the radius is doubled and the height is quartered,

#### Explanation:

A cylinder's volume is equal to the base X height.
Doubling the radius (r) and quartering the height (h) makes the increase (I) equal to the new size / old size
$I = \frac{\left(\pi \cdot {\left(2 r\right)}^{2}\right) \cdot \left(\frac{h}{4}\right)}{\left(\pi \cdot {r}^{2}\right) \cdot \left(h\right)}$
After cancelling the height and pi out, you are left with
$\frac{\frac{4 {r}^{2}}{4}}{r} ^ 2$
which all cancels out to leaving 1, meaning that the volume did not change.