To find the volume of a sphere with a given radius, you can 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 of the sphere,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159,
- [tex]\( r \)[/tex] is the radius of the sphere.
Given the radius [tex]\( r = 3 \)[/tex] meters, we can substitute this value into the formula to find the volume.
Let's calculate it step by step:
1. Cube the radius:
[tex]\[ r^3 = 3^3 = 3 \times 3 \times 3 = 27 \][/tex]
2. Multiply by π:
[tex]\[ \pi \times 27 \approx 3.14159 \times 27 \approx 84.8238 \][/tex]
3. Multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ V = \frac{4}{3} \times 84.8238 \approx 1.33333 \times 84.8238 \approx 113.097 \][/tex]
So, the volume of the sphere is approximately [tex]\( 113.097 \)[/tex] cubic meters.
4. Round to the nearest tenth:
When rounding [tex]\( 113.097 \)[/tex] to the nearest tenth, we look at the hundredths place, which is 9. Since 9 is greater than 5, we round up:
[tex]\[ V \approx 113.1 \][/tex]
Therefore, the volume of the sphere, rounded to the nearest tenth of a cubic meter, is [tex]\( 113.1 \)[/tex] m³.
