Calculate the volume of a cylinder with a height of 25 millimeters and a diameter of 40 millimeters.(1 point)

Responses

40,000π mm3
40,000 pi mm cubed

1,000π mm3
1,000 pi mm cubed

4,000π mm3
4,000 pi mm cubed

10,000π mm3

1 answer

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.

  1. Calculate the radius: The diameter of the cylinder is 40 millimeters, so the radius \( r \) is half of the diameter:

\[ r = \frac{40 , \text{mm}}{2} = 20 , \text{mm} \]

  1. Substitute the radius and height into the volume formula: The height \( h \) is given as 25 millimeters.

\[ V = \pi (20 , \text{mm})^2 (25 , \text{mm}) \]

  1. Calculate \( r^2 \):

\[ (20 , \text{mm})^2 = 400 , \text{mm}^2 \]

  1. Multiply everything together:

\[ V = \pi (400 , \text{mm}^2) (25 , \text{mm}) = 10000 \pi , \text{mm}^3 \]

Therefore, the volume of the cylinder is:

\[ 10,000\pi , \text{mm}^3 \]

The correct response is:

10,000π mm³