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, and
- \( h \) is the height.
First, let's find the radius. The diameter of the cone is given as 6 inches, so the radius \( r \) is half of that:
\[ r = \frac{6}{2} = 3 \text{ inches} \]
The height \( h \) is given as 7 inches. Now, we can plug these values into the volume formula, using \( \pi \) as 3.14:
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
Calculating \( (3)^2 \):
\[ (3)^2 = 9 \]
Now substitute back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
Calculating \( 9 \times 7 \):
\[ 9 \times 7 = 63 \]
Now substitute that back in:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
Calculating \( 3.14 \times 63 \):
\[ 3.14 \times 63 \approx 197.82 \]
Now divide by 3:
\[ V = \frac{197.82}{3} \approx 65.94 \]
So, the volume of the cone is approximately:
\[ \boxed{65.94} \text{ cubic inches} \]
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