Question

Question
Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2 inches. Use 3.14 as an approximation for pi and round your answer to the nearest hundredth, if necessary.(1 point)
Responses

115.55 in.3
115.55 inches cubed

1,222.54 in.3
1,222.54 in cubed

3,260.11 in.3
3,260.11 inches cubed

407.51 in.3

Answer 1

To find the volume of a basketball (which is a sphere) with a diameter of 9.2 inches, we will use the formula for the volume of a sphere:

\[
V = \frac{4}{3} \pi r^3
\]

where \( V \) is the volume and \( r \) is the radius of the sphere.

1. First, we need to find the radius. The radius is half of the diameter:

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

2. Now we can substitute the radius and the value of \(\pi\) (using 3.14) into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (4.6)^3
\]

3. Calculate \(4.6^3\):

\[
4.6^3 = 4.6 \times 4.6 \times 4.6 = 97.336
\]

4. Now substitute this back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 97.336
\]

5. First, calculate \(3.14 \times 97.336\):

\[
3.14 \times 97.336 \approx 306.554944
\]

6. Now calculate \(\frac{4}{3} \times 306.554944\):

\[
V \approx \frac{4 \times 306.554944}{3} \approx \frac{1226.219776}{3} \approx 408.7399253
\]

7. Rounding this to the nearest hundredth:

\[
V \approx 408.74 \text{ in}^3
\]

Based on the provided options, the closest response is:

**407.51 in.³**

It seems there may be a slight discrepancy in the calculations somewhere or in the options provided. However, using the calculated volume of approximately 408.74 in³, none of the responses match precisely. The closest option listed, 407.51 in³, may refer to an approximation or alternate rounding method.