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Step-by-step explanation:
Volume of a sphere is
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
We are given the volume, v, and asked to find the radius, r.
Substitute 4500 ft^3 for v, solve for r.
[tex]4500 = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
Multiply both sides by 3/4 to eliminate 4/3
[tex] \frac{3}{4} \times 4500 = \frac{4}{3} \times \pi \times {r}^{3} \times \frac{3}{4} [/tex]
[tex] \frac{13500}{4} = \pi \times {r}^{3} \: \\ then \: divide \: by \: \pi[/tex]
[tex] \frac{3375}{\pi} = {r}^{3 \: \: take \: the \: cubed \: root \: of \: both \: sides} [/tex]
[tex] \frac{ \sqrt[3]{ {15}^{3} } }{ \sqrt[3]{\pi} } = \sqrt[3]{r} [/tex]
[tex] \frac{15}{ \sqrt[3]{\pi} } = r [/tex]
That approximates to 10.27 ft^3