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Math Help - cone/ surface area/volume..

  1. #1
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    jharkhand
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    cone/ surface area/volume..

    IF h, C , V are height , curved surface and volume of a cone respectively,

    then prove that 3 π V h C h+ 9 V = 0
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  2. #2
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    Quote Originally Posted by snigdha View Post
    IF h, C , V are height , curved surface and volume of a cone respectively,

    then prove that 3 π V h C h+ 9 V = 0
    Hi snighda,

    this is just a practice question for cones.

    Use V=\frac{1}{3}{\pi}r^2h for cone volume

    C={\pi}r\sqrt{r^2+h^2} for cone curved surface area.

    Therefore V^2=\frac{1}{9}{\pi^2}r^4h^2

    C^2={\pi^2}r^2\left(r^2+h^2\right)

    Then

    3{\pi}Vh^2={\pi}^2r^2h^3

    -C^2h^2=-{\pi}^2r^2\left(r^2+h^2\right)h^2

    9V^2={\pi}^2r^4h^2

    If these are added

    {\pi^2}r^2h^2\left(h-\left(h^2+r^2\right)+r^2\right)

    we get zero only if h=1.

    Therefore should your equation have 3{\pi}Vh^3 instead of 3{\pi}Vh^2 ?
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  3. #3
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    umm..i guess you are right..... the correct equation will be 3 pi V h^3 – C h+ 9 V = 0

    thanks...!
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