The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Given that the radius \( r = 12 \) units, we can substitute this value into the formula:
\[ V = \frac{4}{3} \pi (12)^3 \]
Now, calculate \( 12^3 \):
\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1,728 \]
Substituting this back into the volume formula:
\[ V = \frac{4}{3} \pi (1,728) \]
Now, multiply \( 1,728 \) by \( \frac{4}{3} \):
\[ V = \frac{4 \times 1,728}{3} = \frac{6,912}{3} = 2,304 \]
Therefore, the volume of the sphere is:
\[ V = 2,304\pi \text{ cubic units} \]
The correct answer is:
D. \( 2,304\pi \) cubic units