Question

The equation shown is used to find the volume of a cylinder, V , were r is the radius and h is the height. v/r^2 = pi h

which equation correctly shows the radius?
r=√v / πh
r= √v/πh
r=√πh / v
r=√πh/v

Answer 1

`r^{}} = \sqrt{(V)/(\pi h )` is the equation correctly shows the radius.

Option B

Explanation:

The cylinder’ volume (density) indicates how much amount of materials it can able to carry or how much amount of material it can immerse in it. The formula for volume of cylinder is given as:

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

where

V = volume of cylinder

r = radius of cylinder

h = height of cylinder

In order to find radius following simplifications are done:

⇒
`V = \pi r^(2)h`

Keep the factor 'r' in one side and keep other in one side as below,

⇒
`(V)/(\pi h ) = r^(2)`

Taking square root on both sides,

⇒
`\sqrt{r^(2)} = \sqrt{(V)/(\pi h )`

⇒
`r^{}} = \sqrt{(V)/(\pi h )`

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