To create two different cylinders with the same volume but differing dimensions, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Example 1: Cylinder A
Let's take Cylinder A with the following dimensions:
- Radius \( r_1 = 2 \) units
- Height \( h_1 = 5 \) units
Calculating the volume: \[ V = \pi (2^2)(5) = \pi (4)(5) = 20\pi \text{ cubic units} \]
Example 2: Cylinder B
Now, let's create Cylinder B with different dimensions:
- Radius \( r_2 = 1 \) unit
- Height \( h_2 = 20 \) units
Calculating the volume: \[ V = \pi (1^2)(20) = \pi (1)(20) = 20\pi \text{ cubic units} \]
Summary
- Cylinder A: Radius = 2 units, Height = 5 units, Volume = \( 20\pi \) cubic units.
- Cylinder B: Radius = 1 unit, Height = 20 units, Volume = \( 20\pi \) cubic units.
Both cylinders have the same volume of \( 20\pi \) cubic units, but their dimensions are different.