Question

What is the diameter of the sphere?

Answer 1

Remember the equation for the volume of a sphere:

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

Since we know the volume, we can set the formula equal to this value and find our radius, and thus our diameter.

`(4)/(3) \pi r^3 = (32)/(3) \pi`

• Set up

`r^3 = (32)/(3) \cdot (3)/(4)`

• Divide both sides of eqution by
  `(4)/(3) \pi`

`r^3 = 8`

• Multiply right side terms together

`r = 2`

• Take the cube root of both sides

`d = 2(r) = 2(2) = 4`

• Given that
  `d = 2r`, we find
  `d = 4`

Our answer is 4 in.