Question

You purchase a soccer ball that at full capacity measures 8 inches in diameter. How much air can the ball hold if it is pumped to full capacity? Calculate using 3.14 for pi and round to the nearest whole number.(1 point)
Responses

67 inches3
67 inches cubed

268 inches3
268 inches cubed

2,144 inches3
2,144 inches cubed

50 inches3

Answer 1

To calculate the volume of a soccer ball (which is a sphere), we can 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 diameter of the soccer ball is 8 inches, so the radius \( r \) is half of the diameter:

\[
r = \frac{8}{2} = 4 \text{ inches}
\]

2. Next, we plug the radius into the volume formula:

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

3. Now calculate \( (4)^3 \):

\[
(4)^3 = 64
\]

4. Now substitute \( 64 \) back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 64
\]

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

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

6. Now multiply this by \( 64 \):

\[
V \approx 4.18667 \times 64 \approx 267.999
\]

7. Rounding to the nearest whole number, we find:

\[
V \approx 268 \text{ inches}^3
\]

Thus, the soccer ball can hold approximately **268 inches cubed** of air when pumped to full capacity. The correct response is:

**268 inches cubed**