To find the surface area of a basketball, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4 \pi r^2 \]
Where \( r \) is the radius of the sphere. First, we need to find the radius from the diameter. The radius is half of the diameter.
Given the diameter is \( 9.2 \) inches, we calculate the radius as follows:
\[ r = \frac{\text{diameter}}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]
Now, we can substitute the radius into the surface area formula. Using \( \pi \approx 3.14 \):
\[ \text{Surface Area} = 4 \times 3.14 \times (4.6)^2 \]
Calculating \( (4.6)^2 \):
\[ (4.6)^2 = 21.16 \]
Now, substituting this value back into the surface area formula:
\[ \text{Surface Area} = 4 \times 3.14 \times 21.16 \]
Calculating \( 4 \times 3.14 \):
\[ 4 \times 3.14 = 12.56 \]
Now, we multiply \( 12.56 \) by \( 21.16 \):
\[ 12.56 \times 21.16 \approx 266.54 \]
Rounding this to the nearest hundredth gives us:
\[ \text{Surface Area} \approx 266.54 \text{ in}^2 \]
Among the options provided, none of them exactly match this value. However, if we approximate correctly and round accurately, the closest correct approximation for the surface area of the basketball is:
\[ \boxed{265.77 \text{ in}^2} \]