What is the height of a cylinder if its volume is 50π cm³ and the radius is 5 cm?

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. In this case, we know that the volume ( V ) is ( 50\pi ) cm³ and the radius ( r ) is 5 cm.

First, plug the values into the volume formula:

[ 50\pi = \pi (5^2) h ]

This simplifies to:

[ 50\pi = \pi (25) h ]

Next, to eliminate ( \pi ) from both sides, we divide both sides by ( \pi ):

[ 50 = 25h ]

Now, solve for ( h ) by dividing both sides by 25:

[ h = \frac{50}{25} ]

This simplifies to:

[ h = 2 ]

Thus, the height of the cylinder is 2 cm. This aligns with one of the choices given.

Understanding how to manipulate the volume formula allows us to find the height effectively,