Question

The formula V = πr2h gives the volume of a cylinder with radius r and height h. Solve the formula for r. Show your work.

Answer 1

V= pi Times r squared times h
First divide both sides by pi and h
V / pi h = r squared
Square root both sides.

The square root of v /pi times h = r

Answer 2

`r = \sqrt{(V)/(\pi h)}`

Explanation:

The formula to calculate the volume is:

`V = \pi r^(2) h`

Where r is the radius and h the height of the cylinder.

We need to isolate r. First step is to move pi and h, they can go to the other side dividing.

`V = \pi r^(2) h\\ \pi r^(2) h = V\\ \pi r^(2) =(V)/(h)\\r^(2) =(V)/(\pi h)`

Second step, as radius is with an exponent of two, we can use square root.

`r^(2) =(V)/(\pi h)\\\sqrt{r^(2)}  = \sqrt{(V)/(\pi h)}`

Finally, we can isolate radius - r

`r = \sqrt{(V)/(\pi h)}`