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

Question

Responses

4,000π mm3
4,000 pi mm cubed

10,000π mm3
10,000 pi mm cubed

1,000π mm3
1,000 pi mm cubed

40,000π mm3
40,000 pi mm cubed

Answer 1

To calculate the volume \( V \) of a cylinder, you can use the formula:

\[ V = \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height.

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

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

2. The height \( h \) is given as 25 millimeters.

3. Now we can substitute the values into the volume formula:

\[ V = \pi (20)^2 (25) \]

4. Calculate \( (20)^2 \):

\[ (20)^2 = 400 \]

5. Now substitute it back into the equation:

\[ V = \pi (400)(25) \]

6. Multiply \( 400 \) and \( 25 \):

\[ 400 \times 25 = 10,000 \]

7. Finally, put it all together:

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

So, the volume of the cylinder is \( 10,000\pi \text{ mm}^3 \).

The correct response is:

10,000π mm³