Surface Area of Spheres Quick Check

Question

3 of 53 of 5 Items
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

84.64 in.2
84.64 inches squared

1,063.08 in.2
1,063.08 inches squared

265.77 in.2

Answer 1

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

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

First, you need to find the radius of the basketball. The radius is half of the diameter. Given that the diameter is 9.2 inches, the radius \( r \) is:

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

Next, plug the radius into the surface area formula. Using \( \pi \approx 3.14 \):

\[ \text{Surface Area} = 4 \times 3.14 \times (4.6)^2 \]

Now calculate \( (4.6)^2 \):

\[ (4.6)^2 = 21.16 \]

Now substitute that back into the surface area formula:

\[ \text{Surface Area} = 4 \times 3.14 \times 21.16 \]

Calculating \( 4 \times 3.14 \) first:

\[ 4 \times 3.14 = 12.56 \]

Now multiply by 21.16:

\[ \text{Surface Area} = 12.56 \times 21.16 \approx 266.31 \]

Rounding to the nearest hundredth gives:

\[ \text{Surface Area} \approx 266.31 \text{ in}^2 \]

The answer provided in the options is 265.77 in² (as the closest rounded answer).

So, the correct response is:

265.77 in.²