To find the volume of a cone, we can 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.
Given:
- The diameter of the cone is 12 m, so the radius \( r \) is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ m} \]
- The height \( h \) is given as 6 m.
Now, we can substitute these values into the volume formula:
\[ V = \frac{1}{3} \pi (6)^2 (6) \]
Calculating \( (6)^2 \):
\[ (6)^2 = 36 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \pi (36)(6) \]
Calculating \( 36 \times 6 \):
\[ 36 \times 6 = 216 \]
Now we have:
\[ V = \frac{1}{3} \pi (216) \]
Calculating \( \frac{1}{3} \times 216 \):
\[ \frac{216}{3} = 72 \]
Thus, the volume of the cone is:
\[ V = 72\pi \text{ m}^3 \]
So the correct answer is:
C. \( 72\pi \text{ m}^3 \)