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Answer :
To find the volume of a hemisphere with radius [tex]$r = 39.4$[/tex] ft, we start with the formula for the volume of a sphere:
[tex]$$
V_{\text{sphere}} = \frac{4}{3}\pi r^3.
$$[/tex]
Since a hemisphere is exactly half of a sphere, its volume is
[tex]$$
V_{\text{hemisphere}} = \frac{1}{2} \cdot \frac{4}{3}\pi r^3 = \frac{2}{3}\pi r^3.
$$[/tex]
Now, substitute the given radius [tex]$r = 39.4$[/tex] ft into the formula:
[tex]$$
V_{\text{hemisphere}} = \frac{2}{3}\pi (39.4)^3.
$$[/tex]
Evaluating this expression yields a volume of approximately
[tex]$$
128099.45413735336 \text{ cubic feet}.
$$[/tex]
Finally, rounding this value to the nearest tenth gives
[tex]$$
128099.5 \text{ cubic feet}.
$$[/tex]
Thus, the volume of the hemisphere is approximately [tex]$128099.5$[/tex] cubic feet.
[tex]$$
V_{\text{sphere}} = \frac{4}{3}\pi r^3.
$$[/tex]
Since a hemisphere is exactly half of a sphere, its volume is
[tex]$$
V_{\text{hemisphere}} = \frac{1}{2} \cdot \frac{4}{3}\pi r^3 = \frac{2}{3}\pi r^3.
$$[/tex]
Now, substitute the given radius [tex]$r = 39.4$[/tex] ft into the formula:
[tex]$$
V_{\text{hemisphere}} = \frac{2}{3}\pi (39.4)^3.
$$[/tex]
Evaluating this expression yields a volume of approximately
[tex]$$
128099.45413735336 \text{ cubic feet}.
$$[/tex]
Finally, rounding this value to the nearest tenth gives
[tex]$$
128099.5 \text{ cubic feet}.
$$[/tex]
Thus, the volume of the hemisphere is approximately [tex]$128099.5$[/tex] cubic feet.
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