To find the surface area of a sphere, we use the formula:
\[ A = 4\pi r^2 \]
where \( A \) is the surface area and \( r \) is the radius of the sphere.
First, we need to determine the radius from the diameter. The basketball has a diameter of 9.2 inches, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]
Now we can plug the radius into the surface area formula:
\[ A = 4 \pi (4.6)^2 \]
Calculating \( (4.6)^2 \):
\[ (4.6)^2 = 21.16 \]
Now substituting that back into the surface area formula:
\[ A = 4 \pi (21.16) \]
Using \( \pi \approx 3.14 \):
\[ A = 4 \times 3.14 \times 21.16 \]
Calculating \( 4 \times 3.14 \):
\[ 4 \times 3.14 = 12.56 \]
Now multiplying this by \( 21.16 \):
\[ A = 12.56 \times 21.16 \approx 266.58 \]
Rounding to the nearest hundredth, we get:
\[ A \approx 266.58 \text{ in}^2 \]
Given the options, the closest answer is:
265.77 in.²
So the final answer is:
265.77 inches squared.
3 answers