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 [tex]\frac{1}{3}[/tex] 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 = [tex]\frac{1}{3}[/tex] × 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 [tex]\frac{4}{3}[/tex] 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 = [tex]\frac{4}{3}[/tex] × 3.14 × r³ = [tex]\frac{4}{3}[/tex] × π × 8³ = 2,143.5733 cubic cm.
The volume of a half-sphere = [tex]\frac{ 2,143.5733}{2}[/tex] = 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.
