Question

Use the formula for the volume of a sphere to solve the following problem. How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth. (1 point) Responses 113 in.3 113 inches cubed 381.5 in.3 381.5 inches cubed 190.8 in.3 190.8 inches cubed 3,052.1 in.3

Answer 1

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

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

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

1. **Find the radius**: The diameter of the basketball is 9 inches, so the radius \( r \) is half of that:

\[
r = \frac{9}{2} = 4.5 \text{ inches}
\]

2. **Plug the radius into the volume formula**: Using \( \pi \approx 3.14 \):

\[
V = \frac{4}{3} \times 3.14 \times (4.5)^3
\]

3. **Calculate \( (4.5)^3 \)**:

\[
(4.5)^3 = 4.5 \times 4.5 \times 4.5 = 20.25 \times 4.5 = 91.125
\]

4. **Now substitute this back into the volume formula**:

\[
V = \frac{4}{3} \times 3.14 \times 91.125
\]

5. **Calculate \( \frac{4}{3} \times 3.14 \)**:

\[
\frac{4}{3} \times 3.14 \approx 4.18667
\]

6. **Now multiply by 91.125**:

\[
V \approx 4.18667 \times 91.125 \approx 381.5
\]

So, the volume of the basketball, rounded to the nearest tenth, is:

\[
\boxed{381.5 \text{ in}^3}
\]

This matches the option: **381.5 inches cubed**.