To find the ratio of the surface area to the volume for the given sphere, follow these steps:
1. Identify the given values:
[tex]\[
\text{Surface area} = 432 \, \text{m}^2 \\
\text{Volume} = 864 \, \text{m}^3
\][/tex]
2. Calculate the ratio of the surface area to the volume:
[tex]\[
\text{Ratio} = \frac{\text{Surface area}}{\text{Volume}} = \frac{432 \, \text{m}^2}{864 \, \text{m}^3}
\][/tex]
3. Perform the division:
[tex]\[
\text{Ratio} = \frac{432}{864} = 0.5 \, \text{m}^{-1}
\][/tex]
So, the ratio of the surface area to the volume for the sphere is [tex]\(0.5 \, \text{m}^{-1}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(0.5 \, \text{m}^{-1}\)[/tex]
