To determine the volume of a sphere with a given radius, we use the formula for the volume of a sphere:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
In this formula, \( V \) represents the volume and \( r \) represents the radius of the sphere. We are given that the radius \( r \) is 15.
Substituting \( r = 15 \) into the formula:
[tex]\[
V = \frac{4}{3} \pi (15^3)
\][/tex]
Thus, the correct expression from the given options is:
D. \(\frac{4}{3} \pi \left(15^3\right)\)
After performing the computation (raising 15 to the power of 3, multiplying by π, and then multiplying by \(\frac{4}{3}\)), the volume of the sphere is found to be approximately:
14137.166941154068 cubic units.
Therefore, the correct choice is:
D. [tex]\(\frac{4}{3} \pi \left(15^3\right)\)[/tex]
