Question

If h, C and V respectively are the height, the curved surface and volume of cone, then $3\pi V{h}^3-C^2{h}^2+9V^2$ is?

• A. $4\pi r$
• B. $0$
• C. $2\pi rh$
• D. $\pi r^3$

Answer 1

The correct option is B $0$

Given, $r,h,l,C,V$ are radius, height, slant height, curved surface and volume of cone, respectively.

We know, volume of the cone $V=\frac{1}{3}\pi r^{2}h$

and curved surface $C=\pi rl=\pi r\sqrt{h^2+r^2}$

Then, $3\pi V{h}^3-C^2{h}^2+9V^2$

$⟹$ $3\pi$ $\left(\frac{1}{3}\pi r^{2}h\right)$ $h^3-$ $\left(\pi r\sqrt{h^2+r^2}\right)h^2+9$ $(\frac{1}{3}\pi r^{2}h{)}^2$

$⟹$ ${\pi }^2{r}^2{h}^4$ $-{\pi }^2{r}^2{h}^4$ $-{\pi }^2{r}^2{h}^4$ $+{\pi }^2{r}^2{h}^4$ $=0$.