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Timothy Schoonover · Answer 1 · 2022-03-24T05:11:14+0000

Answer:

The volume of the figure is: 60840
$\pi ^3$ , or approximately about 191037.6 ft^3.

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
$(2)/(3)\pi r^3$ , so substituting 39 for r gives us a volume of 39546
$\pi \\\\$ 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
$(\pi r^2h)/3$ , and substituting 39 for r and 42 for h, we obtain a result of 21294
$\pi^3$ , or about 66863.16

Thus, the final volume of the figure is: 60840
$\pi ^3$ , or approximately about 191037.6 ft^3

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