To calculate the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
First, determine the radius. The diameter of the cylinder is 40 millimeters, so the radius \( r \) is half of the diameter:
\[ r = \frac{40 \text{ mm}}{2} = 20 \text{ mm} \]
The height \( h \) is given as 25 millimeters.
Now, substitute the values into the volume formula:
\[ V = \pi (20 \text{ mm})^2 (25 \text{ mm}) \]
Calculating \( (20 \text{ mm})^2 \):
\[ (20 \text{ mm})^2 = 400 \text{ mm}^2 \]
Now substitute this back into the volume calculation:
\[ V = \pi (400 \text{ mm}^2) (25 \text{ mm}) \]
Multiply 400 mm² by 25 mm:
\[ 400 \text{ mm}^2 \times 25 \text{ mm} = 10000 \text{ mm}^3 \]
So the volume of the cylinder is:
\[ V = 10000 \pi \text{ mm}^3 \]
Thus, the correct answer is:
10,000π mm³ (or 10,000 pi mm cubed).