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

2,144 inches3
2,144 inches cubed

50 inches3
50 inches cubed

67 inches3
67 inches cubed

1 answer

To calculate the amount of air the soccer ball can hold at full capacity, we need to determine the volume of a sphere using the formula:

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

Where:

  • \(V\) is the volume,
  • \(\pi\) is approximately 3.14,
  • \(r\) is the radius.

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

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

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 back into the volume equation:

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

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

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

Now multiply by \(\pi\):

\[ V \approx 85.33 \times 3.14 \approx 267.69 \]

Rounding to the nearest whole number gives:

\[ 268 \]

Therefore, the soccer ball can hold approximately 268 inches³ of air.

The correct response is:

268 inches³