To find the volume \( V \) of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
Given:
- The diameter of the cone is 6 inches, so the radius \( r \) is half of that: \[ r = \frac{6}{2} = 3 \text{ inches} \]
- The height \( h \) of the cone is 7 inches.
Now, substitute the values for \( r \), \( h \), and \( \pi \) (using 3.14) into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
First, calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
Now, substitute \( 9 \) into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
Next, calculate \( 9 \times 7 \):
\[ 9 \times 7 = 63 \]
Now substitute \( 63 \) back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
Now compute \( 3.14 \times 63 \):
\[ 3.14 \times 63 = 197.82 \]
Next, divide by 3 to find \( V \):
\[ V = \frac{197.82}{3} \approx 65.94 \]
Therefore, the volume of the cone, rounded to the nearest hundredth, is:
\[ \boxed{65.94} \text{ cubic inches} \]
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