Question

Left cylinder
Right cylinder
Drag the points to create two different cylinders with the same volume. You can change both the height and radius of earth cylinder.

What is the volume of the cylinders?

Answer 1

The volume \( V \) of a cylinder can be calculated using the formula:

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

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a mathematical constant approximately equal to 3.14159.

To create two different cylinders with the same volume, you can adjust the height and radius of each cylinder accordingly. For example:

1. **Cylinder 1**:
- Radius (\( r_1 \)): 2 units
- Height (\( h_1 \)): 5 units

The volume would be:
\[
V_1 = \pi (2^2)(5) = \pi (4)(5) = 20\pi \text{ cubic units}
\]

2. **Cylinder 2**:
- Radius (\( r_2 \)): 1 unit
- Height (\( h_2 \)): 20 units

The volume would be:
\[
V_2 = \pi (1^2)(20) = \pi (1)(20) = 20\pi \text{ cubic units}
\]

Both cylinders have the same volume of \( 20\pi \) cubic units, demonstrating that you can have different combinations of radius and height that yield the same volume. You can create additional pairs of cylinders with the same volume by varying the radius and height.