Question

The formula for the volume of a sphere is V=4/3nr3 . What is the formula solved for r

Answer 1

V = 4/3 π r^3 //Multiply both sides by 3 and divide both sides by 4.

3V/4 = π r^3 //Divide both sides by π

(3V)/(4π) = r^3 //Cube root on both sides.

3√ (3V/4π)

NOTE: 3√ means cube root and not 3 times square root. Everything inside the root is cube root (3V)/(4π).

//Hope it helps.

Answer 2

For this case we have that by definition, the volume of a sphere is given by:

`V = \frac {4} {3} * \pi * r ^ 3`

We must find the solution for "r", clearing:

Multiplying by 3 on both sides of the equation:

`3V = 4 * \pi * r ^ 3`

We divide between
`4 * \pi` on both sides of the equation:

`\frac {3V} {4 \pi} = r ^ 3`

Finally, we apply cubic root on both sides of the equation:

`r = \sqrt [3] {\frac {3V} {4 \pi}}`

Answer:

`r = \sqrt [3] {\frac {3V} {4 \pi}}`