Answer:
The radius of the sphere and cylinder is 2.25 inches.
Step-by-step explanation:
It is given that sphere and a right cylinder have the same radius and volume.
Let the radius of the sphere and cylinder be r.
The volume of the sphere is
[tex]V_1=\frac{4}{3}\pi r^3[/tex]
The volume of the cylinder is
[tex]V_2=\pi r^2h[/tex]
The cylinder has a height of 3 inches.
[tex]V_2=\pi r^2(3)=3\pi r^2[/tex]
[tex]V_1=V_2[/tex]
[tex]\frac{4}{3}\pi r^3=3\pi r^2[/tex]
[tex]4\pi r^3=9\pi r^2[/tex]
[tex]\frac{\pi r^3}{\pi r^2}=\frac{9}{4}[/tex]
[tex]r=\frac{9}{4}=2.25[/tex]
Therefore radius of the sphere and cylinder is 2.25 inches.
