To find the volume of a sphere, we can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
Given that the radius \( r \) is 6 units, we can substitute \( r \) and \( \pi \) (using 3.14 as the approximation):
\[ V = \frac{4}{3} \times 3.14 \times (6)^3 \]
First, calculate \( 6^3 \):
\[ 6^3 = 216 \]
Now substitute that back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 216 \]
Calculate \( \frac{4}{3} \times 216 \):
\[ \frac{4 \times 216}{3} = \frac{864}{3} = 288 \]
Now, multiply by \( 3.14 \):
\[ V = 288 \times 3.14 \approx 904.32 \]
Therefore, the approximate volume of the sphere is:
\[ \boxed{904.32} \text{ cubic units (Option A)} \]