Question

The volume inside of a sphere is V=4πr33 where r is the radius of the sphere. Your group has been asked to rearrange the formula so that it is rewritten to solve for r. Below are various solutions that your group-mates have arrived at. Select the correct one. A r=3V4π−−−√ B r=3V4π−−−√3 C r=3V√34π D r=4V3π−−−√3

Answer 1

Therefore,

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

is the required r

Explanation:

Given:

Volume of inside of the sphere is given as

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

where r is the radius of the sphere

To Find:

r =?

Solution:

We have

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

`3* V=4\pi r^(3) \\\\\therefore r^(3)=(3V)/(4\pi ) \\\\\therefore r=\sqrt[3]{(3V)/(4\pi )} \textrm{which is the expression for r}`

Therefore,

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

is the required r