Question

Find the diameter of a sphere with the volume 7776pi in^3

Answer 1

The diameter is 36 inches

Explanation:

The volume of a sphere is

`(4)/(3) \pi {r}^(3)`

The given sphere has volume

`7776\pi {in}^(3)`

We can now equate the formula to the given volume and solve for r.

`(4)/(3) \pi {r}^(3) = 7776\pi`

`{r}^(3)= 7776\pi * (3)/(4\pi)`

`{r}^(3) = 5832`

`r = \sqrt[3]{5832}`

`r = 18`

The diameter of the sphere is twice the radius.

Hence

`diameter = 2 * 18 = 36in`