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