# How do you prove that the volume of any paraboloid is always half the volume of the circumscribed cylinder?

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Jun 17, 2018

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Simply use the generic formulas to show that whatever specific values are used, the ratio is always 1:2.

#### Explanation:

The calculation of a general parabolic solid volume is described here:

https://math.stackexchange.com/questions/113248/volume-of-a-parabolic-solid

Using the same variable dimensions for the base radius and the height of both the parabola and the cylinder, the two equations can be compared as a ratio. The algebraic solution proves that the 1:2 ratio of Parabolic:Cylinder volumes is correct.

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