EXPLANATION
If the volume of a sphere is 80487 in^3, the diameter would be given by the following relationship:
[tex]\text{Volume}=\frac{4}{3}\cdot\pi\cdot r^3[/tex]
Replacing terms:
[tex]80487=\frac{4}{3}\cdot\pi\cdot r^3[/tex]
Isolating r^3:
[tex]\frac{80487}{\pi}\cdot\frac{3}{4}=r^3[/tex]
Applying the cubic root to both sides:
[tex]\sqrt[]{\frac{80487}{\pi}\cdot\frac{3}{4}}=r[/tex]
Switching sides:
[tex]r=\sqrt[]{\frac{80487}{\pi}\cdot\frac{3}{4}}[/tex]
Multiplying numbers:
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