The volume \( V \) of a cone is calculated using 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, so the radius \( r \) is half of that:
\[ r = \frac{4}{2} = 2 \text{ inches} \]
- The height \( h \) is 9 inches.
Now, substituting these values into the volume formula:
\[ V = \frac{1}{3} \pi (2)^2 (9) \]
Calculating \( (2)^2 \):
\[ (2)^2 = 4 \]
Now substitute it back into the volume equation:
\[ V = \frac{1}{3} \pi (4)(9) \]
Calculating \( 4 \times 9 \):
\[ 4 \times 9 = 36 \]
Now we substitute that into the equation:
\[ V = \frac{1}{3} \pi (36) \]
Now divide 36 by 3:
\[ \frac{36}{3} = 12 \]
So the volume is:
\[ V = 12\pi \text{ in}^3 \]
Therefore, the correct answer is:
12π in.³