Use the formula for the surface area of a sphere to find the surface area of a basketball that has a diameter of 9.2 inches. Use 3.14 pi and round your answer to the nearest hundredth, if necessary.(1 point) Responses 66.44 in.2 66.44 inches squared 84.64 in.2 84.64 inches squared 1,063.08 in.2 1,063.08 inches squared 265.77 in.2

1 answer

The formula for the surface area \(A\) of a sphere is given by:

\[ A = 4 \pi r^2 \]

where \(r\) is the radius of the sphere.

First, we need to find the radius of the basketball. The diameter is given as \(9.2\) inches, so the radius \(r\) is half of the diameter:

\[ r = \frac{9.2}{2} = 4.6 \text{ inches} \]

Now, we can substitute the radius into the surface area formula. Using \(\pi \approx 3.14\), we have:

\[ A = 4 \times 3.14 \times (4.6)^2 \]

Calculating \((4.6)^2\):

\[ (4.6)^2 = 21.16 \]

Now substitute this back into the surface area formula:

\[ A = 4 \times 3.14 \times 21.16 \]

Calculating \(4 \times 3.14\):

\[ 4 \times 3.14 = 12.56 \]

Now, multiply \(12.56\) by \(21.16\):

\[ A \approx 12.56 \times 21.16 \approx 266.25 \]

Rounding to the nearest hundredth, the surface area of the basketball is:

\[ \approx 266.25 \text{ inches squared} \]

Thus, the correct response is:

265.77 in.² (rounding may differ slightly based on precision)