Answer:
The diameter is 36 inches
Step-by-step explanation:
The volume of a sphere is
[tex] \frac{4}{3} \pi {r}^{3} [/tex]
The given sphere has volume
[tex]7776\pi {in}^{3} [/tex]
We can now equate the formula to the given volume and solve for r.
[tex]\frac{4}{3} \pi {r}^{3} = 7776\pi[/tex]
[tex] {r}^{3}= 7776\pi \times \frac{3}{4\pi} [/tex]
[tex] {r}^{3} = 5832[/tex]
[tex]r = \sqrt[3]{5832} [/tex]
[tex]r = 18[/tex]
The diameter of the sphere is twice the radius.
Hence
[tex]diameter = 2 \times 18 = 36in[/tex]
