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, we need to determine the radius. The diameter of the cone is given as 6 inches, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches} \]
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The height \( h \) of the cone is given as 7 inches.
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Now we can substitute the values into the volume formula. Using \( \pi \approx 3.14 \):
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
- First, calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
- Now substitute that back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
- Now calculate \( 9 \times 7 \):
\[ 9 \times 7 = 63 \]
- Substitute that into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
- Now, calculate \( 3.14 \times 63 \):
\[ 3.14 \times 63 = 197.82 \]
- Finally, divide by 3:
\[ V = \frac{197.82}{3} \approx 65.94 \]
Thus, the volume of the cone, rounded to the nearest hundredth, is:
\[ \boxed{65.94} \text{ cubic inches} \]