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)

Question

Responses

268 inches3
268 inches cubed

67 inches3
67 inches cubed

50 inches3
50 inches cubed

2,144 inches3

Answer 1

To calculate the volume of a soccer ball (which can be approximated as a sphere), we can use the formula for the volume $V$ of a sphere:

$$V=\frac{4}{3}\pi r^3$$

Where:

• $\pi$ is approximately 3.14
• $r$ is the radius of the sphere

First, we need to find the radius. Since the diameter of the soccer ball is 8 inches, the radius $r$ would be:

$$r=\frac{d}{2}=\frac{8}{2}=4\text{ inches}$$

Now, plug the radius back into the volume formula:

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

Calculating $(4{)}^3$:

$$(4{)}^3=64$$

Now substitute $r^3$ back into the volume equation:

$$V=\frac{4}{3}\times 3.14\times 64$$

Now calculate $\frac{4}{3}\times 3.14$:

$$\frac{4\times 3.14}{3}=\frac{12.56}{3}\approx 4.18667$$

Now calculate the volume:

$$V\approx 4.18667\times 64\approx 267.99968$$

Rounding to the nearest whole number, we find:

$$V\approx 268\text{ cubic inches}$$

Thus, the air that the ball can hold is:

268 inches³ (or 268 inches cubed).