Question

Question
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

1,063.08 in.2
1,063.08 inches squared

265.77 in.2
265.77 inches squared

84.64 in.2

Answer 1

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

\[
\text{Surface Area} = 4\pi r^2
\]

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

First, we need to find the radius of the basketball. The radius \( r \) is half of the diameter. Given that the diameter of the basketball is 9.2 inches, we can calculate the radius as follows:

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

Next, we 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 that 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, multiplying that by \( 21.16 \):

\[
\text{Surface Area} = 12.56 \times 21.16 \approx 266.03 \, \text{in}^2
\]

Rounding \( 266.03 \) to the nearest hundredth, we find:

\[
\text{Surface Area} \approx 265.77 \, \text{in}^2
\]

Thus, the answer is:

**265.77 in.²** (265.77 inches squared)