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

1,222.54 in.3
1,222.54 in cubed

115.55 in.3
115.55 inches cubed

407.51 in.3
407.51 inches cubed

3,260.11 in.3
3,260.11 inches cubed

Answer 1

To find the volume of a basketball using the formula for the volume of a sphere, we first need the formula:

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

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

Given that the diameter of the basketball is 9.2 inches, we can find the radius:

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

Now we can substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):

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

First, calculate \( (4.6)^3 \):

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

Now we can substitute this value into the volume formula:

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

Now calculate \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.18867
\]

Next, calculate the volume:

\[
V \approx 4.18867 \times 97.336 \approx 407.44 \, \text{in}^3
\]

Rounding to the nearest hundredth, we have:

\[
V \approx 407.44 \, \text{in}^3
\]

Looking at the provided options, the correct response is:

**407.51 in.³**