To calculate the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius of the base of the cone and \( h \) is the height of the cone.
Given:
- The height \( h = 9 \) inches
- The diameter of the cone is 4 inches, which gives us a radius \( r = \frac{4}{2} = 2 \) inches.
Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \pi (2)^2 (9) \]
Calculating \( (2)^2 \) gives us 4, so:
\[ V = \frac{1}{3} \pi (4) (9) \]
Now multiply \( 4 \) by \( 9 \):
\[ 4 \times 9 = 36 \]
So we have:
\[ V = \frac{1}{3} \pi (36) \]
Calculating \( \frac{36}{3} \) gives us 12, thus:
\[ V = 12 \pi \]
Finally, the volume of the cone is:
\[ V = 12\pi \text{ in}^3 \]
The correct response is \( \boxed{12\pi \text{ in}^3} \).