Answer:
The volume of the sphere is [tex]V=18\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]V=27\pi\ ft^{3}[/tex]
substitute
[tex]27\pi=\pi r^{2}h[/tex]
simplify
[tex]27=r^{2}h[/tex]
Remember that
A sphere and a cylinder have the same radius and height
so
The height of cylinder is equal to the diameter of sphere
h=2r
substitute
[tex]27=r^{2}(2r)[/tex]
[tex]13.5=r^{3}[/tex] -----> equation A
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute equation A in the formula of the volume of sphere
[tex]V=\frac{4}{3}\pi (13.5)[/tex]
[tex]V=18\pi\ ft^{3}[/tex]
