Question

The formula for the volume sphere is V=4/3pie r^3 what is the formula solved for r?

Answer 1

The formula for radius of sphere is r = ∛(3V/4π)

or

r = (3V/4π)¹/³

Explanation:

It is given formula for volume of sphere.

Volume of sphere = 4/3 πr³

Where r is the radius of sphere

To find the radius r of sphere

Volume V = 4/3 πr³

r³ = 3V/4π

r = ∛(3V/4π)

Therefore formula for radius of sphere is r = ∛(3V/4π)

or

r = (3V/4π)¹/³

Answer 2

`r = \sqrt[3]{(3V)/(4 \pi)}`

Explanation:

From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.

`V=(4)/(3) \pi r^(3)\\\\ \text{Multiplying both sides by 3/4 we get}\\\\(3V)/(4) = \pi r^(3)\\\\ \text{Dividing both sides by } \pi \\\\ (3V)/(4 \pi) = r^(3)\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{(3V)/(4 \pi)} = r`

Therefore:

`r = \sqrt[3]{(3V)/(4 \pi)}`