To determine the expression that represents the volume of a sphere with a radius of 6 units, we use the formula for the volume of a sphere. The volume \( V \) of a sphere is given by the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where \( r \) is the radius of the sphere.
Given that the radius \( r \) is 6 units, we substitute \( r \) with 6 into the formula:
[tex]\[ V = \frac{4}{3} \pi (6)^3 \][/tex]
Thus, the correct expression representing the volume of the sphere in cubic units is:
[tex]\[
\boxed{\frac{4}{3} \pi (6)^3}
\][/tex]
This is the correct option from the provided choices, which is:
[tex]\[
\frac{4}{3} \pi(6)^3
\][/tex]
