To find the volume of a cone, we 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.
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Calculate the radius: The diameter of the cone is 6 inches, so the radius \( r \) is: \[ r = \frac{6}{2} = 3 \text{ inches} \]
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Use the height: The height \( h \) is given as 7 inches.
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Substitute the values into the volume formula: Using \( \pi \approx 3.14 \): \[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
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Calculate \( (3)^2 \): \[ (3)^2 = 9 \]
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Substitute \( 9 \) into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
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Calculate \( 9 \times 7 \): \[ 9 \times 7 = 63 \]
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Substitute \( 63 \) back into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 63 \]
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Calculate \( 3.14 \times 63 \): \[ 3.14 \times 63 = 197.82 \]
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Finally, divide by 3: \[ V = \frac{197.82}{3} \approx 65.94 \]
Thus, the volume of the cone is approximately:
\[ \boxed{65.94} \text{ cubic inches} \]