Question

What is the radius of a sphere with a volume of 1/6 pie

Answer 1

`\large\boxed{the\ radius\ R=(1)/(2)}`

Explanation:

The formula of a volume of a sphere:

`V=(4)/(3)\pi R^3`

We have

`V=(1)/(6)\pi`

Substitute:

`(4)/(3)\pi R^3=(1)/(6)\pi` divide both sides by π

`(4)/(3)R^3=(1)/(6)` multiply both sides by 3

`3\!\!\!\!\diagup^1\cdot(4)/(3\!\!\!\!\diagup_1)R^3=3\!\!\!\!\diagup^1\cdot(1)/(6\!\!\!\!\diagup_2)`

`4R^3=(1)/(2)` divide both sides by 4

`R^3=(1)/(2):4\\\\R^3=(1)/(2)\cdot(1)/(4)\\\\R^3=(1)/(8)\to R=\sqrt[3]{(1)/(8)}\\\\R=(\sqrt1)/(\sqrt8)\\\\R=(1)/(2)`