The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given:
- Height \( h = 12 \) inches
- Diameter \( d = 8 \) inches
First, we need to find the radius \( r \):
\[ r = \frac{d}{2} = \frac{8}{2} = 4 \text{ inches} \]
Now we can calculate the volume:
\[ V = \pi r^2 h = 3.14 \times (4)^2 \times 12 \]
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
Now substituting back into the volume formula:
\[ V = 3.14 \times 16 \times 12 \]
Calculating \( 16 \times 12 \):
\[ 16 \times 12 = 192 \]
So we have:
\[ V = 3.14 \times 192 \]
Now multiplying this out:
\[ V = 602.88 \text{ cubic inches} \]
Thus, the volume of the cylinder is:
\[ \boxed{602.88 \text{ cubic inches}} \]
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