To determine the radius of a sphere given its volume, we will 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
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159
Given:
[tex]\[ V = 5575.28 \, \text{m}^3 \][/tex]
We need to solve this equation for [tex]\( r \)[/tex]. First, let's isolate [tex]\( r \)[/tex]:
[tex]\[ 5575.28 = \frac{4}{3} \pi r^3 \][/tex]
To isolate [tex]\( r^3 \)[/tex], we multiply both sides of the equation by [tex]\(\frac{3}{4\pi}\)[/tex]:
[tex]\[ r^3 = \frac{3 \cdot 5575.28}{4 \pi} \][/tex]
Next, we take the cube root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \left(\frac{3 \cdot 5575.28}{4 \pi}\right)^{1/3} \][/tex]
After performing the calculation, we find that:
[tex]\[ r \approx 11.000000156148959 \][/tex]
Therefore, the radius of the sphere is approximately 11 meters.
So, the correct answer is:
[tex]\[ \text{D. } 11 \, \text{m} \][/tex]
