Answer :
we are given a sphere and a cylinder with the following conditions:
[tex]r_s=r_c=r[/tex][tex]h=3r[/tex]The volume of the sphere is given by the following formula:
[tex]V_s=\frac{4}{3}\pi r^3[/tex]The volume of the cylinder is given by:
[tex]V_c=\pi r^2h[/tex]Since the height "h" is three times the radius "r", we get_
[tex]V_c=3\pi r^3[/tex]Now we divide both sides by 3:
[tex]\frac{V_c}{3}=\pi r^3[/tex]Now we replace the right sides of the volume of the sphere for its equivalent in the volume of the cylinder:
[tex]V_s=\frac{4}{3}(\frac{V_c}{3})[/tex]Solving:
[tex]V_s=\frac{4}{9}V_c[/tex]Multiplying by 9/4:
[tex]\frac{9}{4}V_s=V_c[/tex]Therefore, the cylinder occupies 9/4 of the volume of the sphere.