Answer:
The volume of the figure is: 60840[tex]\pi ^3[/tex], or approximately about 191037.6 ft^3.
Step-by-step explanation:
This 3D figure can be split into two separate figures, a half-sphere, and a cone.
Let's first try to find the volume of the half-sphere.
The formula for the volume of the half-sphere is [tex]\frac{2}{3}\pi r^3[/tex], so substituting 39 for r gives us a volume of 39546[tex]\pi \\\\[/tex]ft^3, or about 124174.44 ft^3.
Next, let's find the volume of the cone. We see that the radius of the cone is once again 39 ft, and the height of the cone i s just 81-39, or 42 ft.
The volume of a cone is [tex](\pi r^2h)/3[/tex], and substituting 39 for r and 42 for h, we obtain a result of 21294[tex]\pi^3[/tex], or about 66863.16
Thus, the final volume of the figure is: 60840[tex]\pi ^3[/tex], or approximately about 191037.6 ft^3
