The formula for the volume of a cone is V= (1)/(3) \pi r^(2) h Express the formula for the radius, r, of the cone.

Question

The formula for the volume of a cone is

V=
`(1)/(3) \pi r^(2) h`  Express the formula for the radius, r, of the cone.

Answer 1

To express the formula for the radius, r, of a cone, rearrange the volume formula V = 1/3πr²h to solve for r: r = √(3V / (πh)).

Step-by-step explanation:

To express the formula for the radius, r, of a cone, we need to rearrange the volume formula. The original formula is:

V = 1/3πr²h

To isolate r, we can multiply both sides of the equation by 3/π:

3/π * V = r²h

Next, divide both sides of the equation by h:

3V / (πh) = r²

Finally, take the square root of both sides of the equation to solve for r:

r = √(3V / (πh))

Answer 2

First divide both sides by everything that isn't r² to isolate r.
3V/(πh) = r²

Now take the square root of each side:
√[3V/(πh)] = r