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, and \( h \) is the height.
Given:
- Diameter = 40 millimeters
- Height = 25 millimeters
First, we calculate the radius:
\[ r = \frac{\text{Diameter}}{2} = \frac{40 \text{ mm}}{2} = 20 \text{ mm} \]
Now we can 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 it back into the volume formula:
\[ V = \pi (400 \text{ mm}^2) (25 \text{ mm}) \]
Now calculate \( 400 \text{ mm}^2 \times 25 \text{ mm} \):
\[ 400 \text{ mm}^2 \times 25 \text{ mm} = 10000 \text{ mm}^3 \]
Thus, the volume becomes:
\[ V = 10000\pi \text{ mm}^3 \]
Now, looking at the options provided:
- 40,000π mm³
- 40,000 pi mm cubed
- 4,000π mm³
- 4,000 pi mm cubed
- 1,000π mm³
The correct answer:
\[ 10000\pi \text{ mm}^3 \]
It seems that the original options provided do not include \( 10000\pi \text{ mm}^3 \). Therefore, there may have been an error in the options given or the problem setup.
However, \( 10000\pi \text{ mm}^3 \) is the accurate volume of the cylinder.