The volume of a sphere is given by the following formula
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where r represents the radius of the sphere. The diameter of our sphere is 12 inches. The radius is half of the diameter, therefore, the radius of our sphere is 6 inches. Using this radius value on our equation, we have
[tex]V_S=\frac{4}{3}\pi(6)^3=\frac{4}{3}\pi\cdot216=288\pi[/tex]
The volume of a cylinder is given by the following formula
[tex]V=\pi r^2h[/tex]
Where r represents the radius and h the height of the cylinder. The diameter of our cylinder is 10 inches. The radius is half of the diameter, therefore, the radius of our cylinder is 5 inches. The height is also given and it is 12 inches. Using those values on the formula, we have
[tex]V_C=\pi\cdot(5)^2\cdot12=\pi\cdot25\cdot12=300\pi[/tex]
Comparing the volumes, we have
[tex]300\pi>288\pi\Rightarrow V_C>V_S[/tex]
The volume of the cylinder is greater than the volume of the sphere.
