Question

Rewrite the following equation in terms of $r$:

$V=\pi (R^2-r^2)h;r$

• A. $r=\sqrt{R^2-\frac{V}{\pi h}}$
• B. $r=\sqrt{R^2+\frac{V}{\pi h}}$
• C. $r=\sqrt{2R^2-\frac{V}{\pi h}}$
• D. none of these

Answer 1

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

Given equation is: $V=\pi (R^2-r^2)h$
$V=(R^{2}h\pi -\pi r^{2}h)$
$\pi r^{2}h=\pi R^{2}h-V$
$r^2=\frac{\pi R^{2}h-V}{\pi h}$
$\therefore r=\sqrt{\frac{\pi R^{2}h-V}{\pi h}}=\sqrt{R^2-\frac{V}{\pi h}}$