To find the surface area of the basketball, start by identifying its diameter, which is 9 inches.
1. Find the radius:
The radius is half of the diameter. Therefore, the radius is:
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{9}{2} = 4.5 \text{ inches}
\][/tex]
2. Calculate the surface area of the sphere:
The formula for the surface area of a sphere is:
[tex]\[
\text{Surface Area} = 4 \pi r^2
\][/tex]
Substitute the radius into the formula:
[tex]\[
\text{Surface Area} = 4 \pi (4.5)^2
\][/tex]
3. Compute the value:
First, calculate [tex]\( (4.5)^2 \)[/tex]:
[tex]\[
(4.5)^2 = 20.25
\][/tex]
Now, multiply by [tex]\( 4 \pi \)[/tex]:
[tex]\[
4 \pi \times 20.25 \approx 4 \times 3.14159 \times 20.25 \approx 254.46900494077323 \text{ square inches}
\][/tex]
4. Round to the nearest hundredth:
The surface area rounded to the nearest hundredth would be:
[tex]\[
254.47 \text{ square inches}
\][/tex]
Thus, the surface area of the basketball is about:
[tex]\[
\boxed{254.47}
\][/tex] square inches.
