A Cone Around a Cube

★ 8/10Extrema calculus solid geometry Solids of Revolution

Problem

A cube $ABCD\text{-}A_1B_1C_1D_1$ has edge length $2$ . The vertices $A_1, B_1, C_1, D_1$ lie on the lateral surface of a cone, and the vertices $A, B, C, D$ lie in the plane of the cone's base. Find the minimum possible volume of the cone.

Answer

Solution

Difficulty	8/10
Topics	Extrema, calculus, solid geometry, Solids of Revolution

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