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We are given that the volume of the sphere is approximately \(320 \, \text{in}^3\), and the question asks to approximate its surface area. To find the surface area, we need to follow these steps:

1. **Use the volume formula of a sphere**:
   \[
   V = \frac{4}{3} \pi r^3
   \]
   where \(V\) is the volume and \(r\) is the radius.

2. **Solve for the radius \(r\)**:
   Given \(V = 320 \, \text{in}^3\), we can solve for \(r\):
   \[
   320 = \frac{4}{3} \pi r^3
   \]
   Multiply both sides by \(\frac{3}{4\pi}\) to isolate \(r^3\):
   \[
   r^3 = \frac{320 \times 3}{4\pi} \approx \frac{960}{12.5664} \approx 76.39
   \]
   Now, take the cube root of both sides to find \(r\):
   \[
   r \approx \sqrt[3]{76.39} \approx 4.27 \, \text{in}
   \]

3. **Use the surface area formula of a sphere**:
   \[
   A = 4 \pi r^2
   \]
   Substituting \(r \approx 4.27 \, \text{in}\):
   \[
   A \approx 4 \pi (4.27)^2 \approx 4 \times 3.1416 \times 18.23 \approx 229 \, \text{in}^2
   \]

Therefore, the surface area is approximately **226 in²** (option B).

Would you like more details on the steps? Here are some related questions:

1. How do you solve for the radius of a sphere if the volume is known?
2. Can you explain why we use the cube root to find the radius?
3. What is the relationship between the volume and surface area of a sphere?
4. How would the surface area change if the volume were doubled?
5. Why is \(\pi\) used in the formulas for spheres?

**Tip:** When working with spheres, the volume formula involves \(r^3\), while the surface area formula involves \(r^2\). Keep this distinction in mind when solving problems!

The volume of a sphere is about 320 in³. Approximately, what is its surface area?

Learn how to calculate the surface area of a sphere with a given volume of 320 in³. This geometry problem uses key formulas such as volume (V = (4/3)πr³) and surface area (A = 4πr²), suitable for students in Grades 8-10.

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