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Answer:
The height is 8.83 units
Step-by-step explanation:
Recall that [tex]V_{sphere}=\frac{4}{3}\pi r^3[/tex]. Since the height of a sphere is just twice the radius, then we need to solve for r and multiply by 2 to get the height of the cylinder:
[tex]V_{sphere}=\frac{4}{3}\pi r^3[/tex]
[tex]361=\frac{4}{3}\pi r^3[/tex]
[tex]1083=4\pi r^3[/tex]
[tex]\frac{1083}{4\pi}=r^3[/tex]
[tex]\sqrt[3]{\frac{1083}{4\pi}}=r[/tex]
[tex]h=2r[/tex]
[tex]h=2\sqrt[3]{\frac{1083}{4\pi}}[/tex]
[tex]h\approx8.83[/tex]