b. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. In this case, the radius of the cone is 3 inches and the height is also 5 inches, so the volume of the cone is:
V = (1/3)π(3^2)(5) = 15π cubic inches
c. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base and h is the height of the cylinder. In this case, the radius is 3 inches and the height is 5 inches, so the volume of the cylinder is:
V = π(3^2)(5) = 45π cubic inches
The fraction of the cylinder's volume that is the cone's volume can be found by dividing the volume of the cone by the volume of the cylinder:
(15π) / (45π) = 1/3
Therefore, the cone's volume is 1/3 of the cylinder's volume.