Question

3. 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, and make certain to show your work. Hint: you may need to find the volume of the component shapes.

Answer 1

The volume of the prop is calculated to be 2,712.96 cubic inches.

Explanation:

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying
`(1)/(3)` with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone :
`V=\pi r^(2) (h)/(3)` =
`3.14 * 9^(2) * (14)/(3)` = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying
`(4)/(3)` with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere =
`V=(4)/(3) \pi r^(3)` =
`(4)/(3) * 3.14 * 9^(3)` = 3,052.08 cubic inches.

The volume of the half-sphere =
`(3,052.08)/(2)` = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.