To find 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,
- \( \pi \) is a constant approximately equal to 3.14.
Given the diameter of the cone is 6 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{6}{2} = 3 \text{ inches} \]
The height \( h \) is given as 7 inches. Now, substitute these values into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot (3)^2 \cdot 7 \]
First, calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
Now substitute that back into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot 9 \cdot 7 \]
Now multiply \( 9 \cdot 7 \):
\[ 9 \cdot 7 = 63 \]
Thus, the volume becomes:
\[ V = \frac{1}{3} \cdot 3.14 \cdot 63 \]
Next, calculate \( 3.14 \cdot 63 \):
\[ 3.14 \cdot 63 = 197.82 \]
Now calculate \( \frac{1}{3} \cdot 197.82 \):
\[ V = \frac{197.82}{3} \approx 65.94 \]
Finally, rounding to the nearest hundredth, the volume of the cone is:
\[ \boxed{65.94} \text{ cubic inches} \]