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 \(\( V \)\) of a sphere is given by:
\(\[ V = \frac{4}{3} \pi r^3 \]\)
where:
- \(\( V \)\) is the volume,
- \(\( \pi \)\) (pi) is a constant approximately equal to 3.14159,
- \(\( r \)\) is the radius of the sphere.
Let's break down the steps to solve for the volume:
1. Identify the radius: The radius \(\( r \)\) 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 \(\( r^3 \)\):
\(\[
(4.5)^3 = 4.5 \times 4.5 \times 4.5
\]\)
\(\[
(4.5)^3 = 91.125
\]\)
3. Multiply by \(\( \pi \)\): Next, multiply the cubed radius by \(\( \pi \)\):
\(\[
\pi \cdot 91.125 \approx 3.14159 \cdot 91.125
\]\)
\(\[
3.14159 \cdot 91.125 \approx 286.1637
\]\)
4. Multiply by \(\( \frac{4}{3} \)\): Finally, multiply the result by \(\( \frac{4}{3} \)\):
\(\[
\frac{4}{3} \cdot 286.1637 \approx 381.7035074111598
\]\)
Thus, the volume of air that the beach ball holds is approximately 381.7035 cubic inches.
