To find the volume of a volleyball with a radius of 10.1 cm, we will use the formula for the volume [tex]\( V \)[/tex] of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the sphere,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159.
Given that the radius [tex]\( r \)[/tex] is 10.1 cm, we'll substitute [tex]\( r \)[/tex] with 10.1 cm in the formula:
[tex]\[ V = \frac{4}{3} \pi (10.1)^3 \][/tex]
First, calculate [tex]\( (10.1)^3 \)[/tex]:
[tex]\[ 10.1^3 = 10.1 \times 10.1 \times 10.1 = 1030.301 \][/tex]
Next, substitute [tex]\( (10.1)^3 \)[/tex] and [tex]\( \pi \)[/tex] into the formula:
[tex]\[ V = \frac{4}{3} \pi \times 1030.301 \][/tex]
[tex]\[ V = \frac{4}{3} \times 3.14159 \times 1030.301 \][/tex]
Perform the multiplication:
[tex]\[ V \approx \frac{4}{3} \times 3.14159 \times 1030.301 = 4315.714736781622 \][/tex]
Finally, round the volume to the nearest tenth:
[tex]\[ V \approx 4315.7 \, \text{cm}^3 \][/tex]
Therefore, the volume of the volleyball is [tex]\( 4315.7 \, \text{cm}^3 \)[/tex].
