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

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

Answer 2

Answer: V = 2712.94 cubic inches.

Step-by-step 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 = $\frac{1}{3}.B.h$

B is area of the base

h is height

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

V₁ = $\frac{1}{3}$.π.$r^{2}$.h

V₁ = $\frac{1}{3}$ . 3.14 . $9^{2}$ . 14

V₁ = 1186.9 cubic inches

Volume of Half-Sphere:

V₂ = $\frac{2}{3}$.π.$r^{3}$

V₂ = $\frac{2}{3}$ . 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