Remember the equation for the volume of a sphere:
[tex]V = \dfrac{4}{3} \pi r^3[/tex]
Since we know the volume, we can set the formula equal to this value and find our radius, and thus our diameter.
[tex]\dfrac{4}{3} \pi r^3 = \dfrac{32}{3} \pi[/tex]
[tex]r^3 = \dfrac{32}{3} \cdot \dfrac{3}{4}[/tex]
- Divide both sides of eqution by [tex]\frac{4}{3} \pi[/tex]
[tex]r^3 = 8[/tex]
- Multiply right side terms together
[tex]r = 2[/tex]
- Take the cube root of both sides
[tex]d = 2(r) = 2(2) = 4[/tex]
- Given that [tex]d = 2r[/tex], we find [tex]d = 4[/tex]
Our answer is 4 in.
