To calculate the volume \( V \) of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Height \( h = 25 \) mm
- Diameter \( d = 40 \) mm, so the radius \( r = \frac{d}{2} = \frac{40}{2} = 20 \) mm
Now, we can substitute these values into the volume formula:
\[ V = \pi (20)^2 (25) \]
Calculating \( (20)^2 \):
\[ (20)^2 = 400 \]
Now, substituting that back into the formula:
\[ V = \pi \times 400 \times 25 \]
Calculating \( 400 \times 25 \):
\[ 400 \times 25 = 10,000 \]
So, the volume \( V \) becomes:
\[ V = 10,000\pi , \text{mm}^3 \]
Thus, the correct response is:
10,000π mm³ (or 10,000 pi mm cubed).