A solid machine part is to be manufactured as shown in the figure The part is made by cutting a small cone off the top of a larger cone The small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches prior to being cut What is the volume of the resulting part illustrated in the fiqure?

Answer:The exact volume of the part is 390pi in.^3Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3Step-by-step explanation:Find the volume of the large cone and the volume of the small cone. The subtract the small volume from the large volume.Large cone:V = (1/3)(pi)r^2hV = (1/3)(pi)(9 in.)^2(15 in.)V = 405pi in.^3Small cone:V = (1/3)(pi)r^2hV = (1/3)(pi)(3 in.)^2(5 in.)V = 15pi in.^3Difference in volumes:volume of part = 405pi in.^3 - 15pi in.^3 = 390pi in.^3The exact volume of the part is 390pi in.^3Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3