Question

A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 1/3x. Find the height of the cone in terms of y.

Answer 1

Great question! I had this question in Geometry on Edmentum.

Answer: Height of cone = 3y

Step-by-step explanation:

We know that the cylinder and the cone have the same volume. The cylinder has radius x and height y. We will make use of the formulas:

Volume of cylinder = πr²h

Volume of cone = 1/3πr²h

Since the cone has radius 1/3x, we will have to make its height 3 times of y (the height of the cylinder) to make both the cylinder and the cone have the same volume.

So, the height of the cone is equal to 3y.

Hope this helps, and have a wonderful day! :D

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