To determine the volume of air that a beach ball with a radius of 4.5 inches holds, we can use the formula for the volume of a sphere. The formula for the volume [tex]\( V \)[/tex] of a sphere is given by:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159,
- [tex]\( r \)[/tex] is the radius of the sphere.
Let's break down the steps to solve for the volume:
1. Identify the radius: The radius [tex]\( r \)[/tex] of the beach ball is given as 4.5 inches.
2. Cube the radius: To cube the radius means to raise it to the power of three. This is written mathematically as [tex]\( r^3 \)[/tex]:
[tex]\[
(4.5)^3 = 4.5 \times 4.5 \times 4.5
\][/tex]
[tex]\[
(4.5)^3 = 91.125
\][/tex]
3. Multiply by [tex]\( \pi \)[/tex]: Next, multiply the cubed radius by [tex]\( \pi \)[/tex]:
[tex]\[
\pi \cdot 91.125 \approx 3.14159 \cdot 91.125
\][/tex]
[tex]\[
3.14159 \cdot 91.125 \approx 286.1637
\][/tex]
4. Multiply by [tex]\( \frac{4}{3} \)[/tex]: Finally, multiply the result by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[
\frac{4}{3} \cdot 286.1637 \approx 381.7035074111598
\][/tex]
Thus, the volume of air that the beach ball holds is approximately 381.7035 cubic inches.
