Question

If $V=\pi (R^2-r^2)h$, then $r$ can be written as

• A. $\sqrt{\frac{\pi R^{2}h-V}{\pi h}}$
• B. $\sqrt{\frac{\pi Rh-V}{\pi h}}$
• C. $\sqrt{\frac{{\pi }^2{R}^{2}h+V}{\pi h}}$
• D. $\sqrt{\frac{{\pi }^2{R}^{2}h-V}{\pi h}}$

Answer 1

The correct option is A $\sqrt{\frac{\pi R^{2}h-V}{\pi h}}$

Given equation is: $V=\pi (R^2-r^2)h$

$V=\pi {hR}^2-\pi {hr}^2$

$\pi h{r}^2=\pi {hR}^2-V$

$r^2=\frac{\pi h{R}^2-V}{\pi h}$

$\therefore r=\sqrt{\frac{\pi h{R}^2-V}{\pi h}}$