Question

If h,S and V denote respectively the height,curved surface area and volume of a right circular cone,then $3\pi V{h}^3-S^2{h}^2+9V^2$ is equal to

• A. 8
• B. 0
• C. 4 $\pi$
• D. 32 ${\pi }^2$

Answer 1

The correct option is B

0

h=height , S=curved surface area and V=volume of the cone

Let r be the radius of the cone,then

$S=\pi rl,wherel=\sqrt{r^2+h^2}\therefore S=\pi r\sqrt{r^2+h^2}V=\frac{1}{3}\pi r^{2}hNow,3\pi V{h}^3-S^2{h}^2+9V^2=3\pi \left(\frac{1}{3}\pi r^{2}h\right)h^3-{\pi }^2{r}^2(r^2+h^2)h^2+9\left(\frac{1}{9}{\pi }^2{r}^4{h}^2\right)={\pi }^2{r}^2{h}^4-{\pi }^2{r}^4{h}^2-{\pi }^2{r}^2{h}^4+{\pi }^2{r}^4{h}^2=0$