The volume of the prop is calculated to be 2,712.96 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 [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 9 inches and the height is 14 inches.
The volume of the cone : [tex]V=\pi r^{2} \frac{h}{3}[/tex] = [tex]3.14 \times 9^{2} \times \frac{14}{3}[/tex] = 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 [tex]\frac{4}{3}[/tex] 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 = [tex]V=\frac{4}{3} \pi r^{3}[/tex] = [tex]\frac{4}{3} \times 3.14 \times 9^{3}[/tex] = 3,052.08 cubic inches.
The volume of the half-sphere = [tex]\frac{3,052.08}{2}[/tex] = 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.
