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

268 inches3
268 inches cubed

50 inches3
50 inches cubed

67 inches3
67 inches cubed

2,144 inches3

Answer 1

To calculate the volume of a soccer ball (which is a sphere) at full capacity, we can use the formula for the volume of a sphere:

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

Where:
- \( V \) is the volume,
- \( \pi \) is approximately 3.14,
- \( r \) is the radius of the sphere.

First, we determine the radius from the diameter. The diameter of the soccer ball is 8 inches, so the radius \( r \) is half of that:

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

Now we can substitute the radius into the volume formula:

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

Calculating \( (4)^3 \):

\[
(4)^3 = 64
\]

Now substituting that back into the volume formula:

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

Calculating \( \frac{4}{3} \times 64 \):

\[
\frac{4}{3} \times 64 \approx 85.33 \quad (\text{as } \frac{256}{3} = 85.33)
\]

Now multiplying by \( \pi \):

\[
V \approx 85.33 \times 3.14 \approx 267.08
\]

Rounding to the nearest whole number:

\[
V \approx 267
\]

**Conclusion: The closest option is 268 inches cubed.**