You purchase a soccer ball that at full capacity measures 8 inches in diameter.

Question

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)
• 50 inches3
• 67 inches3
• 2, 144 inches3
• 268 inches3

Answer 1

To calculate the volume of a soccer ball at full capacity, we can use the formula for the volume of a sphere:

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

where $r$ is the radius of the sphere.

First, we need to find the radius. The diameter of the ball is 8 inches, so the radius $r$ is:

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

Now we can substitute the radius into the volume formula using $\pi \approx 3.14$:

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

Calculating $(4{)}^3$:

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

Now substitute this value 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 multiplying by $\pi$:

$$V\approx 85.33\times 3.14\approx 267.66$$

Rounding to the nearest whole number:

$$V\approx 268{\text{ inches}}^3$$

Thus, the soccer ball can hold approximately 268 inches³ of air. The correct answer is:

• 268 inches³.