Answer :

To find the volume of a hemisphere with a diameter of 37.6 meters, follow these steps:

1. Calculate the Radius:
- The radius of a sphere is half of its diameter. Since the diameter is 37.6 meters, divide it by 2 to get the radius:
[tex]\[
\text{Radius} = \frac{37.6}{2} = 18.8 \text{ meters}
\][/tex]

2. Volume of a Sphere:
- The formula for the volume of a sphere is:
[tex]\[
\text{Volume of a sphere} = \frac{4}{3} \pi r^3
\][/tex]
- We need the volume of just a hemisphere, which is exactly half the volume of a sphere.

3. Volume of a Hemisphere:
- The formula for the volume of a hemisphere is:
[tex]\[
\text{Volume of a hemisphere} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3
\][/tex]
- Substitute the radius (18.8 meters) into this formula. You will need to calculate the following:
[tex]\[
\text{Volume of a hemisphere} = \frac{2}{3} \times \pi \times (18.8)^3
\][/tex]

4. Compute the Volume:
- Performing the calculation gives a volume of approximately:
[tex]\[
13916.568 \text{ cubic meters}
\][/tex]

5. Round to the Nearest Tenth:
- Round the volume to the nearest tenth:
[tex]\[
\text{Volume rounded} = 13916.6 \text{ cubic meters}
\][/tex]

Therefore, the volume of the hemisphere is approximately 13,916.6 cubic meters when rounded to the nearest tenth.

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Rewritten by : Barada