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

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- Nov 23rd 2006, 12:36 AManjanaSurface 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?:confused:

- Nov 23rd 2006, 01:57 AMtopsquark
$\displaystyle V = \pi r^2 L$

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

So what is our new L'?

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

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

Cancelling the common $\displaystyle \pi r^2$:

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

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

$\displaystyle L' = 0.826 L$

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

-Dan