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

then provethat 3 πVh² – C² h²+ 9 V² = 0

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- Feb 20th 2010, 08:07 AMsnigdhacone/ surface area/volume..
*IF h*,*C*,*V are height*,*curved surface and volume of a cone respectively,*

*then prove*that 3 π*V*h² – C² h²+ 9 V² = 0 - Feb 20th 2010, 08:38 AMArchie Meade
Hi snighda,

this is just a practice question for cones.

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

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

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

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

Then

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

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

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

If these are added

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

we get zero only if h=1.

Therefore should your equation have $\displaystyle 3{\pi}Vh^3$ instead of $\displaystyle 3{\pi}Vh^2$ ? - Feb 21st 2010, 07:19 AMsnigdha
umm..i guess you are right..... the correct equation will be 3 pi

*V*h^3 – C² h²+ 9 V² = 0

thanks...!