To calculate the volume \( V \) of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
Given the diameter of the cone is 4 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{4}{2} = 2 \text{ inches} \]
The height \( h \) of the cone is given as 9 inches.
Now plug in the values into the volume formula:
\[ V = \frac{1}{3} \pi (2)^2 (9) \]
Calculating \( (2)^2 \):
\[ (2)^2 = 4 \]
Now substitute that back into the volume formula:
\[ V = \frac{1}{3} \pi (4)(9) \]
Now calculate \( 4 \times 9 \):
\[ 4 \times 9 = 36 \]
So now we have:
\[ V = \frac{1}{3} \pi (36) = 12\pi \]
Thus, the volume of the cone is:
\[ \boxed{12\pi \text{ in}^3} \]
The correct response is: 12π in.³.