# Math Help - Surface Area And Volumes

1. ## Surface Area And Volumes

if the radius of cylinder is increased by 10%,how much will the length be decreased so that volume remains the same?

2. Originally Posted by anjana
if the radius of cylinder is increased by 10%,how much will the length be decreased so that volume remains the same?
$V = \pi r^2 L$

So if we increase r by 10% $r \to \frac{11r}{10}$

So what is our new L'?

$V = \pi r^2 L = \pi \left ( \frac{11r}{10} \right )^2 L'$

$\pi r^2 L = \pi \frac{121}{100} r^2 L'$

Cancelling the common $\pi r^2$:
$L = \frac{121}{100} L'$

$L' = \frac{100}{121} L$

$L' = 0.826 L$

or we have reduced the length to about 82.6% of it's original value.

-Dan