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Thread: Find Ratios Between Volumes + Extra

  1. #1

    Question Find Ratios Between Volumes + Extra

    I got this question for homework and I'm not sure how to do it:

    a) Find the ratio between the volume of a cone and the volume of a sphere.

    b) Find the values of r and h if the ratio in a) = 1/3.

    Thanks a lot.
    Last edited by tomirlik; Mar 4th 2008 at 10:28 AM.
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  2. #2
    Senior Member topher0805's Avatar
    Jan 2008
    Volume of a cone is $\displaystyle \frac {1}{3}\pi r^2h$, Where r is the radius of the base and h is the height of the cone.

    Volume of a sphere is $\displaystyle \frac {4}{3}\pi r^3$.

    To find the ratio, divide the cone formula by the sphere formula:

    $\displaystyle \frac {\frac {1}{3}\pi r^2h}{\frac {4}{3}\pi r^3}$

    Factor out $\displaystyle \frac {1}{3}\pi r^2$ from the top and bottom:

    $\displaystyle \frac {(\frac {1}{3}\pi r^2)(h)}{(\frac {1}{3}\pi r^2)(4r)}$

    So your final answer is:

    $\displaystyle \frac {h}{4r}$
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