Question

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 4,000π mm3 4,000 pi mm cubed 1,000π mm3

Answer 1

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.