# cone/ surface area/volume..

• Feb 20th 2010, 08:07 AM
snigdha
cone/ 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 AM
Quote:

Originally Posted by snigdha
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

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

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

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

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

$\displaystyle {\pi^2}r^2h^2\left(h-\left(h^2+r^2\right)+r^2\right)$
Therefore should your equation have $\displaystyle 3{\pi}Vh^3$ instead of $\displaystyle 3{\pi}Vh^2$ ?