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Thread: Surface Area And Volumes

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

    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
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