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, and \(h\) is the height.
Given:
- Diameter = 6 inches, so the radius \(r\) is half of the diameter: \[ r = \frac{6}{2} = 3 \text{ inches} \]
- Height \(h = 7\) inches.
Now, plug the values into the volume formula using \(\pi \approx 3.14\):
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
Calculating \( (3)^2 \):
\[ (3)^2 = 9 \]
Now substituting it back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
Calculating \(9 \times 7\):
\[ 9 \times 7 = 63 \]
Now substitute again:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
Calculating \(3.14 \times 63\):
\[ 3.14 \times 63 = 197.82 \]
Now divide by 3:
\[ V = \frac{197.82}{3} \approx 65.94 \]
Thus, the volume of the cone to the nearest hundredth is
\[ \boxed{65.94} \text{ cubic inches.} \]
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