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.
Given the radius \( r = 15 \) inches, we can plug in the value:
\[ V = \frac{4}{3} \pi (15)^3 \]
Calculating \( (15)^3 \):
\[ 15^3 = 3375 \]
Now substitute back into the volume formula:
\[ V = \frac{4}{3} \pi (3375) \]
Now, multiplying \( \frac{4}{3} \) by \( 3375 \):
\[ V = \frac{13500}{3} \pi = 4500 \pi \]
Now, using \( \pi \approx 3.14 \):
\[ V \approx 4500 \times 3.14 = 14130 \]
Thus, the volume of the exercise ball is approximately:
\[ \boxed{14,130} \]