To determine the ratio of the surface area to the volume for the given sphere, we should follow these steps:
1. Identify the given values:
- Surface area [tex]\(A = 588 \, m^2\)[/tex]
- Volume [tex]\(V = 1372 \, m^3\)[/tex]
2. Calculate the ratio of the surface area to the volume:
[tex]\[
\text{Ratio} = \frac{\text{Surface Area}}{\text{Volume}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Ratio} = \frac{588 \, m^2}{1372 \, m^3}
\][/tex]
3. Simplify the ratio:
Performing the division:
[tex]\[
\text{Ratio} \approx 0.42857142857142855 \, m^{-1}
\][/tex]
This numerical result is obtained by dividing 588 by 1372.
4. Compare the calculated ratio with the provided options:
- Option A: [tex]\(0.04 \, m^{-1}\)[/tex]
- Option B: [tex]\(0.4 \, m^{-1}\)[/tex]
- Option C: [tex]\(0.02 \, m^{-1}\)[/tex]
- Option D: [tex]\(0.2 \, m^{-1}\)[/tex]
Among these options, the value closest to the calculated ratio [tex]\(0.42857142857142855 \, m^{-1}\)[/tex] is:
- Option B: [tex]\(0.4 \, m^{-1}\)[/tex]
5. Conclusion:
The ratio of the surface area to the volume for the given sphere is approximately [tex]\(0.4 \, m^{-1}\)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{0.4 \, m^{-1}} \][/tex]
