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The volume of a cone with base radius
and height
is
Similarly, the volume of a sphere with radius
is
We know that and that
So, we can set up the following equation:
We can simplify the common denominator 3, and pi appearing on both sides:
We can divide both sides by 4:
Without further information, this is all we can say: the cubed radius of the sphere is the same as 24 times the squared radius of the cone.