The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14159.
Given:
- \( r = 12 \) mm
- \( h = 50 \) mm
Plugging in the values:
\[ V = \pi (12 , \text{mm})^2 (50 , \text{mm}) \]
Calculating \( (12 , \text{mm})^2 \):
\[ (12 , \text{mm})^2 = 144 , \text{mm}^2 \]
Now substituting back into the volume formula:
\[ V = \pi (144 , \text{mm}^2)(50 , \text{mm}) = \pi (7200 , \text{mm}^3) \]
Now, using \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 7200 , \text{mm}^3 \approx 22619.47 , \text{mm}^3 \]
Therefore, the volume of the cylinder is approximately \( 22619.47 , \text{mm}^3 \).