To determine the volume of a hemisphere with a diameter of 3.7 meters, follow these steps:
1. Determine the radius:
- The radius [tex]\( r \)[/tex] of a hemisphere is half its diameter.
- Given diameter [tex]\( d = 3.7 \)[/tex] meters, the radius [tex]\( r \)[/tex] can be calculated as:
[tex]\[
r = \frac{d}{2} = \frac{3.7}{2} = 1.85 \text{ meters}
\][/tex]
2. Use the formula for the volume of a hemisphere:
- The volume [tex]\( V \)[/tex] of a hemisphere is given by the formula:
[tex]\[
V = \frac{2}{3} \pi r^3
\][/tex]
3. Calculate the volume:
- Substituting [tex]\( r = 1.85 \)[/tex] meters into the formula, we get:
[tex]\[
V = \frac{2}{3} \pi (1.85)^3
\][/tex]
- After evaluating the expression, the volume is approximately:
[tex]\[
V \approx 13.260924390190317 \text{ cubic meters}
\][/tex]
4. Round the volume to the nearest tenth:
- The calculated volume, 13.260924390190317 cubic meters, rounded to the nearest tenth, is:
[tex]\[
V \approx 13.3 \text{ cubic meters}
\][/tex]
Thus, the volume of the hemisphere with a diameter of 3.7 meters, rounded to the nearest tenth, is 13.3 cubic meters.
