To calculate 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,
- \( h \) is the height,
- \( \pi \) is a constant (approximately 3.14).
Given the diameter of the cone is 6 inches, the radius \( r \) will be half of the diameter:
\[ r = \frac{6}{2} = 3 \text{ inches} \]
The height \( h \) is given as 7 inches. Now substitute \( r \), \( h \), and \( \pi \) into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
First, calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
Now substitute this back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
Next, calculate \( 9 \times 7 \):
\[ 9 \times 7 = 63 \]
Now substitute this back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
Now calculate \( 3.14 \times 63 \):
\[ 3.14 \times 63 = 197.82 \]
Now, divide this result by 3 to find the volume:
\[ V = \frac{197.82}{3} = 65.94 \]
Finally, round to the nearest hundredth, so the volume of the cone is:
\[ \boxed{65.94} \text{ cubic inches} \]
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