Video: Finding the Volumes of Cones and Cylinders

A cone has a volume of 486 cubic centimeters. What is the volume of a cylinder that has the same radius and height as the cone?

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Video Transcript

A cone has a volume of 486 cubic centimeters. What is the volume of a cylinder that has the same radius and height as the cone?

The volume of a cone can be calculated using the formula one-third multiplied by 𝜋𝑟 squared ℎ. The volume of a cylinder can be calculated by using the formula 𝜋𝑟 squared ℎ.

In this question, we’re told that the volume of the cone is 486 cubic centimeters. This means that one-third multiplied by 𝜋𝑟 squared ℎ equals 486. Multiplying both sides of this equation by three gives us 𝜋𝑟 squared ℎ is equal to 486 multiplied by three. 486 multiplied by three is equal to 1458.

As 𝜋𝑟 squared ℎ is the formula for the volume of a cylinder, we can say that, in this case, the volume of the cylinder is 1458. This means that a cylinder with the same radius and height as a cone of volume 486 cubic centimeters will have a volume of 1458 cubic centimeters.

We can go one step further when comparing cones and cylinders with the same radius and height. The volume of the cylinder will always be three times the volume of the cone.

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