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, and \( \pi \) is approximately 3.14.
- Find the radius: The diameter of the cone is 6 inches, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches} \]
- Plug in the values: The height \( h \) is given as 7 inches. Now, substitute \( r \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot (3)^2 \cdot 7 \]
- Calculate \( r^2 \):
\[ r^2 = 3^2 = 9 \]
- Now substitute \( r^2 \) into the volume formula:
\[ V = \frac{1}{3} \cdot 3.14 \cdot 9 \cdot 7 \]
- Calculate \( 9 \cdot 7 = 63 \):
\[ V = \frac{1}{3} \cdot 3.14 \cdot 63 \]
- Calculate \( 3.14 \cdot 63 \):
\[ 3.14 \cdot 63 = 197.82 \]
- Now calculate \( \frac{1}{3} \cdot 197.82 \):
\[ V = \frac{197.82}{3} \approx 65.94 \]
So, the volume of the cone is approximately \( \boxed{65.94} \) cubic inches, rounded to the nearest hundredth.
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