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

50 inches3
50 inches cubed

67 inches3
67 inches cubed

2,144 inches3
2,144 inches cubed

268 inches3

1 answer

To find the volume of the soccer ball, which is a sphere, we can use the formula for the volume \( V \) of a sphere:

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

where \( r \) is the radius of the sphere.

Given that the diameter of the soccer ball is 8 inches, we can calculate the radius as follows:

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

Now we can substitute the radius and \( \pi \) into the volume formula:

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

First, calculate \( (4 \text{ inches})^3 \):

\[ (4 \text{ inches})^3 = 4 \times 4 \times 4 = 64 \text{ cubic inches} \]

Now substitute this value back into the volume formula:

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

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

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

Now, multiply this result by \( 3.14 \):

\[ V \approx 85.33 \times 3.14 \approx 267.82 \]

Rounding this to the nearest whole number gives:

\[ V \approx 268 \]

Thus, the soccer ball can hold approximately 268 inchesĀ³ of air when pumped to full capacity.

The correct answer is 268 inches cubed.