The volume \( V \) of a sphere is calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere. Given that the radius \( r = 9 \) cm, we can substitute this value into the formula:
\[ V = \frac{4}{3} \pi (9)^3 \]
Calculating \( 9^3 \):
\[ 9^3 = 729 \]
Now substituting back into the volume formula:
\[ V = \frac{4}{3} \pi (729) \]
Multiplying \( \frac{4}{3} \) by \( 729 \):
\[ V = \frac{2916}{3} \pi \]
\[ V = 972 \pi \]
Thus, the volume of the sphere is
\[ \boxed{972\pi} \text{ cm}^3. \]
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