To find the surface area of a sphere, we can use the formula:
\[ \text{Surface Area} = 4 \pi r^2 \]
where \( r \) is the radius of the sphere.
First, we need to calculate the radius of the basketball. The diameter is given as 9.2 inches, so the radius \( r \) is half of that:
\[ r = \frac{9.2}{2} = 4.6 \text{ inches} \]
Next, 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 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 multiply by \( 21.16 \):
\[ \text{Surface Area} = 12.56 \times 21.16 \approx 266.6896 \]
Rounding this to the nearest hundredth gives:
\[ \text{Surface Area} \approx 266.69 \text{ in}^2 \]
Looking at the options provided, it seems that the closest approximation to our calculated surface area, rounded correctly and considering what was provided in the choices, would be:
265.77 in.²
So the correct answer is 265.77 inches squared.
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