To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.
First, we need to find the radius of the cone. The diameter is given as 6 inches, so the radius \(r\) is half of the diameter:
\[ r = \frac{6}{2} = 3 \text{ inches} \]
Next, we have the height \(h\) of the cone, which is given as 7 inches.
Now we can plug the values for \(r\), \(h\), and \(\pi\) (using \(3.14\)) into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
Calculating \( (3)^2 \):
\[ (3)^2 = 9 \]
Substituting this back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
Now calculate \(9 \times 7\):
\[ 9 \times 7 = 63 \]
Substituting this back gives:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
Calculating \(3.14 \times 63\):
\[ 3.14 \times 63 = 197.82 \]
Now calculate \(\frac{1}{3} \times 197.82\):
\[ V = \frac{197.82}{3} \approx 65.94 \]
Rounding to the nearest hundredth, we find:
\[ \boxed{65.94} \]
Thus, the volume of the cone is approximately \(65.94\) cubic inches.