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

265.77 in.2
265.77 inches squared

1,063.08 in.2
1,063.08 inches squared

84.64 in.2
84.64 inches squared

1 answer

To find the surface area of a sphere, you can use the formula:

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

where \( S \) is the surface area and \( r \) 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:

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

Now we can substitute the radius into the surface area formula using \( \pi \approx 3.14 \):

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

Calculating \( (4.6)^2 \):

\[ (4.6)^2 = 21.16 \]

Now substitute back into the surface area formula:

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

Calculating \( 4 \times 3.14 = 12.56 \):

\[ S = 12.56 \times 21.16 \approx 266.02 \]

Rounding this to the nearest hundredth gives:

\[ S \approx 266.02 \]

Among the options provided, the closest value to our calculation is:

265.77 in.²

So the answer is: 265.77 inches squared.