Answer: V = 2712.94 cubic inches.
Step-by-step explanation: The prop is formed with two objects: cone and half of a sphere. To calculate the volume, find the volume of the cone and the half-sphere and add them together.
Volume of Cone:
V₁ = [tex]\frac{1}{3}.B.h[/tex]
B is area of the base
h is height
Since the cone has its base as a circle, the volume will be:
V₁ = [tex]\frac{1}{3}[/tex].π.[tex]r^{2}[/tex].h
V₁ = [tex]\frac{1}{3}[/tex] . 3.14 . [tex]9^{2}[/tex] . 14
V₁ = 1186.9 cubic inches
Volume of Half-Sphere:
V₂ = [tex]\frac{2}{3}[/tex].π.[tex]r^{3}[/tex]
V₂ = [tex]\frac{2}{3}[/tex] . 3.14 . [tex]9^{3}[/tex]
V₂ = 1526.04 cubic inches
Total Volume:
V = V₁ + V₂
V = 1186.9 + 1526.04
V = 2712.94 cubic inches
The volume of the prop is V = 2712.94 cubic inches
