Question

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 figure? A. 15 cubic inches B. 155 cubic inches C. 390 cubic inches D. 405 cubic inches

Answer 1

Answer:

1225.23 inches³ OR  390π inches³ ⇒ answer C

Step-by-step explanation:

* Lets revise the rule of the volume of any cone

- The volume of the cone = 1/3 × area of the base × its height

- The base of the cone is a circle

- Area of the circle = πr² , where r is the radius of the circle

- The volume of the cone = 1/3 × πr² × its height

* Lets solve the problem

∵ The radius of the small cone is 3 inches

∵ Its height is 5 inches

∴ The volume of the small cone = 1/3 × π (3)² × 5 = 47.12 inches³

∵ The radius of the larger cone is 9 inches

∵ Its height is 15 inches

∴ The volume of the large cone = 1/3 × π (9)² × 15 = 1272.35 inches³

- The small cone is cutting from the large cone , then the volume of

  the resulting part is the difference between their volumes

∵ The volume of the resulting part = Large volume - small volume

∴ The volume of the resulting part = 1272.35 - 47.12 = 1225.23 inches³

∴ The volume of the resulting part is 1225.23 inches³ OR 390π inches³