Question

The volume (V) of a cylinder can be determined by using the formula V=πr2h, where r= the radius of the base, and h= the height of the cylinder. What is the result of solving this equation for r?

Answer 1

The volume formula for a cylinder can be solved for the radius as:.
`r=\sqrt{(V)/(\pi h)}$` . Option b is the right choice.

We want to isolate r in the formula
`$V=\pi r^2 h$`. Here's how the options work:

- a.
`$r=\sqrt{(h)/(\pi V)}$` : This is incorrect. Dividing by V is not a valid step.

- b.
`$r=\sqrt{(V)/(\pi h)}$` : This is correct! Rearranging the formula, we can get
`$r^2=(V)/(\pi h)$`, and then take the square root of both sides to solve for r.

- c.
`$r=\sqrt{(\pi)/(h V)}$` : This is incorrect. Dividing by V is not valid.

- d.
`$r=(h)/(\pi V)$` : This is incorrect. Dividing by V is not valid.

Therefore, the correct option is b.
`$r=\sqrt{(V)/(\pi h)}$`.

Question:-

The volume of a cylinder is given by
`$V=\pi r^2 h$` wher r is the radius of the circular base and h is the height. Solve this formula for r.

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

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

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

d.
`$r=(h)/(\pi V)$`