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 answer

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.