To determine how much air the beach ball can hold, we need to find the volume of the sphere using the given formula [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex]. Here are the steps to calculate it:
1. Identify the given diameter:
The diameter of the beach ball is 12 inches.
2. Calculate the radius:
The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \text{ inches}
\][/tex]
3. Use the formula for the volume of a sphere:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
Plugging in the values:
[tex]\[
V = \frac{4}{3} \times \pi \times (6)^3
\][/tex]
4. Compute the radius cubed:
[tex]\[
6^3 = 6 \times 6 \times 6 = 216
\][/tex]
5. Substitute [tex]\(\pi \approx 3.14159\)[/tex] into the volume formula:
[tex]\[
V = \frac{4}{3} \times 3.14159 \times 216
\][/tex]
6. Calculate the volume:
[tex]\[
V \approx \frac{4}{3} \times 3.14159 \times 216
\][/tex]
[tex]\[
V \approx 904.78 \text{ cubic inches}
\][/tex]
Therefore, the beach ball can hold approximately [tex]\( 904.78 \)[/tex] cubic inches of air.
