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

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Multiple Choice

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,

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,

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