a) Make $$ r $$ the subject of the formula in $$ V=\frac{1}{3} \pi r^{2} h $$

Question

UpStudy AI · Accepted Answer

To make $$ r $$ the subject of the formula in the equation $$ V = \frac{1}{3} \pi r^{2} h $$, we will follow these steps:

1. Multiply both sides by $$ 3 $$ to eliminate the fraction:
   $$
   3V = \pi r^{2} h
   $$

2. Divide both sides by $$ \pi h $$ to isolate $$ r^{2} $$:
   $$
   r^{2} = \frac{3V}{\pi h}
   $$

3. Take the square root of both sides to solve for $$ r $$:
   $$
   r = \sqrt{\frac{3V}{\pi h}}
   $$

Thus, the expression for $$ r $$ in terms of $$ V $$ and $$ h $$ is:
$$
r = \sqrt{\frac{3V}{\pi h}}
$$
$$ r = \sqrt{\frac{3V}{\pi h}} $$

a) Make the subject of the formula in