Question

Find the radius of a sphere with a volume of 4.57 cubic centimeters.

The radius is ___ centimeters.

Answer 1

`radius` ≈
`1.029`
`cm`

Explanation:

Knowing that the formula for the volume of a sphere is:
`(4)/(3)\pi r^(3)`

We can set the equation equal to 4.57.

`(4)/(3)\pi r^(3)`
`=4.57`

We divide both sides by
`((4)/(3)\pi)` so we can get
`r` by itself.

`r^(3) =(4.57)/((4)/(3) \pi )`

We simplify and get:

`r^(3) =(13.71)/(4\pi )`

Taking the cube root of both sides, we then get the radius:

`r=\sqrt[3]{(13.71)/(4\pi ) }`

The approximate answer comes out to be:

`r`≈
`1.029`