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Math Help - Express h interms of x

  1. #1
    Senior Member Mukilab's Avatar
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    Express h interms of x

    The radius of the base of a cone is x cm and its height is h cm
    The radius of a sphere is 2x cm
    The v olume of the cone and the vilume of the sphere are equal
    Express h in terms of x

    So

    \frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi r^{3}\rightarrow \text{cancel out pi and 1/3} \rightarrow x^2h=4*4x^2\rightarrow x^2h=16x^3\rightarrow h=16x^3-x^2=x^2(16x-1) note: I replaced the r with the x and 2x from circle and cone. Am I correct?
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by Mukilab View Post
    The radius of the base of a cone is x cm and its height is h cm
    The radius of a sphere is 2x cm
    The v olume of the cone and the vilume of the sphere are equal
    Express h in terms of x

    So

    \frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi r^{3}\rightarrow \text{cancel out pi and 1/3} \rightarrow x^2h=4*4x^2\rightarrow x^2h=16x^3\rightarrow h=16x^3-x^2=x^2(16x-1) note: I replaced the r with the x and 2x from circle and cone. Am I correct?
    \frac{\pi}{3} x^2 h = \frac{4\pi}{3} (2x)^3<br />

    x^2 h = 4 (2x)^3

    x^2 h = 32 x^3

    h = 32x
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  3. #3
    Senior Member Mukilab's Avatar
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    thanks, I should be more careful with my powers :P
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