I need measurements for 2 different cylinders that have the exact same amount of volume but have 2 completely different measurements. And What is the volume for the cylinders in Pi? Thank you

1 answer

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.