To find the volume \( V \) of the cylinder using the formula \( V = \pi r^2 h \), we need the radius \( r \) and the height \( h \).
Given:
- Diameter of the base of the cylinder = 4 inches
- Height of the cylinder = 12 inches
First, we need to calculate the radius. The radius \( r \) is half of the diameter:
\[ r = \frac{4 \text{ in}}{2} = 2 \text{ in} \]
Now, we can plug the values into the volume formula:
\[ V = \pi r^2 h \]
Substituting \( r = 2 \) in, \( h = 12 \) in, and using \( \pi \approx 3.14 \):
\[ V = 3.14 \times (2 \text{ in})^2 \times 12 \text{ in} \]
Calculating \( (2 \text{ in})^2 \):
\[ (2 \text{ in})^2 = 4 \text{ in}^2 \]
Now substitute that back into the volume equation:
\[ V = 3.14 \times 4 \text{ in}^2 \times 12 \text{ in} \]
Calculating \( 4 \text{ in}^2 \times 12 \text{ in} \):
\[ 4 \text{ in}^2 \times 12 \text{ in} = 48 \text{ in}^3 \]
Now, substitute this into the equation for volume:
\[ V = 3.14 \times 48 \text{ in}^3 \]
Calculating \( 3.14 \times 48 \):
\[ 3.14 \times 48 = 150.72 \]
So, the volume \( V \) of the cylinder is:
\[ V = 150.72 \text{ in}^3 \]
Therefore, the final answer, rounded to the hundredth's place, is:
\[ \boxed{150.72 \text{ in}^3} \]