The volume of the prop is calculated to be 1,875.6 cubic inches.
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 with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 8 inches and the height is 12 inches.
The volume of the cone: 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 with π and the cube of the radius (r³).
Here the radius is 8 inches. We take π as 3.14.
The volume of a full sphere cubic inches.
The volume of the half-sphere cubic inches.
Step 4:
The total volume = The volume of the cone + The volume of the half sphere,
The total volume = cubic inches.
Rounding this off, we get the volume of the prop as 1,875.6 cubic inches.