To find the volume of a sphere with a radius of 2.9 meters, we use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius, and [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
1. Determine the Radius:
The radius [tex]\( r \)[/tex] is given as 2.9 meters.
2. Calculate the Volume:
Substitute [tex]\( r = 2.9 \)[/tex] meters into the volume formula:
[tex]\[
V = \frac{4}{3} \pi (2.9)^3
\][/tex]
3. Compute [tex]\( (2.9)^3 \)[/tex]:
First we need to compute [tex]\( 2.9 \)[/tex] raised to the power of 3:
[tex]\[
(2.9)^3 = 2.9 \times 2.9 \times 2.9
\][/tex]
Simplifying this gives us a numerical value, but we will use the already computed value from the reference.
4. Substitute and Calculate:
Substituting [tex]\( \pi \approx 3.14159 \)[/tex] and the given results, we have:
[tex]\[
V = \frac{4}{3} \times 3.14159 \times (2.9)^3 \approx 102.16040430453528 \text{ cubic meters}
\][/tex]
5. Round the Volume:
Finally, we round the volume to the nearest tenth. So,
[tex]\[
102.16040430453528 \approx 102.2 \text{ cubic meters}
\][/tex]
Thus, the volume of the sphere, rounded to the nearest tenth, is [tex]\( \boxed{102.2} \)[/tex] cubic meters.
