If the volume of a cylinder is 100π cm³ and the radius is 5 cm, what is the height?

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:

[

V = \pi r^2 h

]

where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height. Given that the volume ( V ) is ( 100\pi ) cm³ and the radius ( r ) is 5 cm, we can substitute these values into the volume formula:

[

100\pi = \pi (5^2) h

]

First, we simplify the equation:

[

100\pi = \pi (25) h

]

Next, we can divide both sides of the equation by ( \pi ) (assuming ( \pi ) is not zero):

[

100 = 25h

]

To isolate ( h ), we divide both sides by 25:

[

h = \frac{100}{25} = 4

]

Thus, the height of the cylinder is 4 cm.

Therefore, the calculation confirms that the correct answer reflects the proper application of the volume formula for a cylinder, leading to a height of