If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.

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Solution

In the given problem, we are given a cone and a sphere which have equal volumes. The dimensions of the two are;

Radius of the cone (r_c) = r

Radius of the sphere (r_s) = 2r

Now, let the height of the cone = h

Here, Volume of the sphere = volume of the cone

Further, solving for h

Therefore, the height of the cone is.

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