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, 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 1,875.6 cubic cm.

Step-by-step 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 $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 8 cm and the height is 12 cm.

The volume of the cone = $\frac{1}{3}$ × 3.14 × 8 × 8 × 12 = 803.84 cubic cm.

Step 3; The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³). Here the radius is 8cm. We take π as 3.14.

The volume of a full sphere = $\frac{4}{3}$ × 3.14 × r³ = $\frac{4}{3}$ × π × 8³ = 2,143.5733 cubic cm.

The volume of a half-sphere = $\frac{ 2,143.5733}{2}$ = 1,071.7866 cubic cm.

Step 4; The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 803.84 cubic cm + 1,071.7866 cubic cm = 1,875.6266 cubic cm. By rounding this off to the nearest tenth we get 1,875.6 cubic cm.