Question

A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

Answer 1

Answer: V = 2712.94 cubic inches.

Explanation: The prop is formed with two objects: cone and half of a sphere. To calculate the volume, find the volume of the cone and the half-sphere and add them together.

Volume of Cone:

V₁ =
`(1)/(3).B.h`

B is area of the base

h is height

Since the cone has its base as a circle, the volume will be:

V₁ =
`(1)/(3)`.π.
`r^(2)`.h

V₁ =
`(1)/(3)` . 3.14 .
`9^(2)` . 14

V₁ = 1186.9 cubic inches

Volume of Half-Sphere:

V₂ =
`(2)/(3)`.π.
`r^(3)`

V₂ =
`(2)/(3)` . 3.14 .
`9^(3)`

V₂ = 1526.04 cubic inches

Total Volume:

V = V₁ + V₂

V = 1186.9 + 1526.04

V = 2712.94 cubic inches

The volume of the prop is V = 2712.94 cubic inches

Answer 2

3.14 x 9^2 x 14/3 = 1186.92

4/3 x 3.14 x 9^3 = 1526.04

1186.92 + 1526.04 = 2712.96 = 2713 cubic inches