Question

The radius of a sphere whose volume is 12 π cubic cm is??

Answer 1

`\sqrt[3]{9}` or approximately 2.08 cm

Explanation:

The volume of a sphere is

V = 4/3 pi r^3

12 pi = 4/3 pi r^3

Divide each side by pi

12 = 4/3 r^3

Multiply each side by 3/4

12 *3/4 = 3/4 * 4/3 r^3

9 = r^3

Take the cube root of each side

9 ^ 1/3 = r^3 ^ 1/3

9 ^ 1/3 = r

The radius is the cube root of 9

or approximately 2.080083823

Answer 2

Given a radius
`r`, the volume of a sphere is given by

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

We can solve this formula for the radius, given the volume:

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

We can plug our value for the volume to get the radius:

`r=\sqrt[3]{(3\cdot 12\pi)/(4\pi)}=\sqrt[3]{9}`