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.

Answer 1

To calculate the volume of a soccer ball, which is spherical in shape, 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, and
- \( r \) is the radius of the sphere.

Given that the diameter of the soccer ball is 8 inches, we can find the radius:

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

Now we can substitute the radius into the volume formula:

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

First, calculate \( 4^3 \):

\[
4^3 = 64
\]

Now substitute this value into the formula:

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

Next, calculate \( \frac{4}{3} \times 64 \):

\[
\frac{4 \times 64}{3} = \frac{256}{3} \approx 85.33
\]

Now, multiply by \( 3.14 \):

\[
V \approx 85.33 \times 3.14 \approx 267.7232
\]

Finally, rounding to the nearest whole number gives:

\[
V \approx 268
\]

Therefore, the volume of air the soccer ball can hold when pumped to full capacity is approximately **268 cubic inches**.