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Answer :
We start with a hemisphere whose diameter is given as [tex]$37.6$[/tex] m. The steps to find the volume are as follows:
1. Determine the radius, [tex]$r$[/tex]. Since the diameter is twice the radius,
[tex]$$
r = \frac{37.6}{2} = 18.8 \text{ m}.
$$[/tex]
2. The formula for the volume of a hemisphere is:
[tex]$$
V = \frac{2}{3} \pi r^3.
$$[/tex]
3. Substitute the value of the radius into the formula:
[tex]$$
V = \frac{2}{3} \pi (18.8)^3.
$$[/tex]
4. Evaluating this expression gives:
[tex]$$
V \approx 13916.568493809198 \text{ cubic meters}.
$$[/tex]
5. Finally, rounding the result to the nearest tenth of a cubic meter, we obtain:
[tex]$$
V \approx 13916.6 \text{ m}^3.
$$[/tex]
Thus, the volume of the hemisphere is approximately [tex]$13916.6$[/tex] cubic meters.
1. Determine the radius, [tex]$r$[/tex]. Since the diameter is twice the radius,
[tex]$$
r = \frac{37.6}{2} = 18.8 \text{ m}.
$$[/tex]
2. The formula for the volume of a hemisphere is:
[tex]$$
V = \frac{2}{3} \pi r^3.
$$[/tex]
3. Substitute the value of the radius into the formula:
[tex]$$
V = \frac{2}{3} \pi (18.8)^3.
$$[/tex]
4. Evaluating this expression gives:
[tex]$$
V \approx 13916.568493809198 \text{ cubic meters}.
$$[/tex]
5. Finally, rounding the result to the nearest tenth of a cubic meter, we obtain:
[tex]$$
V \approx 13916.6 \text{ m}^3.
$$[/tex]
Thus, the volume of the hemisphere is approximately [tex]$13916.6$[/tex] cubic meters.
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