To find the volume of a regulation volleyball with a diameter of 21 cm, we will follow these steps:
1. Determine the radius of the volleyball:
The radius (\(\( r \)\)) is half of the diameter.
\(\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{21 \, \text{cm}}{2} = 10.5 \, \text{cm}
\]\)
2. Use the formula for the volume of a sphere:
The formula for the volume (\(\( V \)\)) of a sphere is:
\(\[
V = \frac{4}{3} \pi r^3
\]\)
Given that \(\( \pi \)\) is 3.14 and the radius \(\( r \)\) is 10.5 cm, we can plug these values into the formula.
3. Calculate the volume:
\(\[
V = \frac{4}{3} \times 3.14 \times (10.5)^3
\]\)
First, we compute \(\( (10.5)^3 \)\):
\(\[
(10.5)^3 = 10.5 \times 10.5 \times 10.5 = 1157.625
\]\)
Next, we multiply this result by \(\( \pi \)\) and the fraction \(\( \frac{4}{3} \)\):
\(\[
V = \frac{4}{3} \times 3.14 \times 1157.625
\]\)
\(\[
V \approx \frac{4}{3} \times 3.14 \times 1157.625 = 4846.59 \, \text{cm}^3
\]\)
4. Round the volume to the nearest whole cubic centimeter:
\(\[
4846.59 \approx 4847 \, \text{cm}^3
\]\)
So, the approximate volume of the volleyball is \(\( 4847 \, \text{cm}^3 \)\).
