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, \( \pi \) is approximately 3.14, \( r \) is the radius, and \( h \) is the height of the cone.
- First, find the radius of the cone. The diameter is 6 inches, so the radius \( r \) is half of that:
\[ r = \frac{6}{2} = 3 \text{ inches} \]
- Next, plug the radius and height into the volume formula. The height \( h \) is given as 7 inches:
\[ V = \frac{1}{3} \times 3.14 \times (3)^2 \times 7 \]
- Calculate \( (3)^2 \):
\[ (3)^2 = 9 \]
- Substitute that back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]
- Calculate \( 9 \times 7 \):
\[ 9 \times 7 = 63 \]
- Now substitute that into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 63 \]
- Calculate \( 3.14 \times 63 \):
\[ 3.14 \times 63 \approx 197.82 \]
- Finally, divide that by 3 to find the volume:
\[ V = \frac{197.82}{3} \approx 65.94 \]
Therefore, the volume of the cone is approximately 65.94 cubic inches.