To find the volume of a sphere, we use the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
Given that the radius [tex]\( r \)[/tex] of the sphere is 4 centimeters, we substitute [tex]\( r = 4 \)[/tex] into the formula:
[tex]\[
V = \frac{4}{3} \pi (4)^3
\][/tex]
First, calculate [tex]\( 4^3 \)[/tex]:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
Next, substitute [tex]\( 4^3 = 64 \)[/tex] into the volume formula:
[tex]\[
V = \frac{4}{3} \pi \times 64
\][/tex]
Now, multiply [tex]\( \frac{4}{3} \)[/tex] and 64:
[tex]\[
\frac{4}{3} \times 64 = \frac{256}{3}
\][/tex]
So the volume of the sphere is:
[tex]\[
V = \frac{256}{3} \pi
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{256}{3} \pi}
\][/tex]
