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