To determine which expression gives the volume of a sphere with radius 15, we need to recall the formula for the volume of a sphere. The volume [tex]\(V\)[/tex] of a sphere is given by:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\(r\)[/tex] is the radius of the sphere.
In this problem, the radius [tex]\( r \)[/tex] is 15. Substituting this value into the formula, we get:
[tex]\[ V = \frac{4}{3} \pi (15)^3 \][/tex]
Thus, the correct expression for the volume of a sphere with radius 15 is:
[tex]\[ \boxed{\frac{4}{3} \pi (15^3)} \][/tex]
The correct choice among the given options is:
D. [tex]\(\frac{4}{3} \pi\left(15^3\right)\)[/tex].
