The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
In your case, the height \( h \) is 8 and the base radius \( r \) is 4. We can calculate the volume as follows:
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Calculate the base area: \[ \text{Base Area} = \pi r^2 = \pi (4^2) = \pi (16) = 16\pi \]
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Calculate the volume: \[ V = \text{Base Area} \times h = 16\pi \times 8 = 128\pi \]
Thus, the volume of the cylinder with height 8 and radius 4 is:
\[ V = 128\pi \text{ cubic units} \]
To create another cylinder with the same volume, choose different values for height and radius such that their product gives the same volume \( 128\pi \).
For example, if we take a radius of 2:
- Set the radius \( r = 2 \).
- Use the volume formula to determine the corresponding height \( h \): \[ V = \pi r^2 h = 128\pi \] \[ \pi (2^2) h = 128\pi \] \[ 4\pi h = 128\pi \] \[ h = \frac{128}{4} = 32 \]
So, another cylinder with radius 2 and height 32 also has a volume of \( 128\pi \).
This gives us two different cylinders:
- Cylinder 1: Radius = 4, Height = 8
- Cylinder 2: Radius = 2, Height = 32
Both have a volume of \( 128\pi \). You can experiment with other combinations as well (for example, using a radius of 1 or 3, and solving for height accordingly).