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Answer :
To find the volume of a hemisphere with a radius of 39.4 feet, you can follow these steps:
1. Understand the Formula for a Sphere's Volume:
The formula to calculate the volume of a full sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( r \)[/tex] is the radius.
2. Calculate the Volume of the Full Sphere:
Substitute the radius (39.4 ft) into the formula:
[tex]\[
V = \frac{4}{3} \pi (39.4)^3
\][/tex]
3. Calculate the Volume of the Hemisphere:
Since a hemisphere is half of a sphere, divide the volume of the full sphere by 2:
[tex]\[
V_{\text{hemisphere}} = \frac{1}{2} \times V_{\text{sphere}}
\][/tex]
4. Round the Volume to the Nearest Tenth:
After calculating the hemisphere's volume using the above steps, you round the result to the nearest tenth.
By following these steps, we find that the volume of the hemisphere, rounded to the nearest tenth, is approximately [tex]\(128099.5 \, \text{cubic feet}\)[/tex].
1. Understand the Formula for a Sphere's Volume:
The formula to calculate the volume of a full sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( V \)[/tex] is the volume and [tex]\( r \)[/tex] is the radius.
2. Calculate the Volume of the Full Sphere:
Substitute the radius (39.4 ft) into the formula:
[tex]\[
V = \frac{4}{3} \pi (39.4)^3
\][/tex]
3. Calculate the Volume of the Hemisphere:
Since a hemisphere is half of a sphere, divide the volume of the full sphere by 2:
[tex]\[
V_{\text{hemisphere}} = \frac{1}{2} \times V_{\text{sphere}}
\][/tex]
4. Round the Volume to the Nearest Tenth:
After calculating the hemisphere's volume using the above steps, you round the result to the nearest tenth.
By following these steps, we find that the volume of the hemisphere, rounded to the nearest tenth, is approximately [tex]\(128099.5 \, \text{cubic feet}\)[/tex].
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