Height of cylinder: 2

Radius of cylinder bottom: 1.

Height of equilateral cone: 3 (We study the shaft section, and then the height of equilateral triangle is three times the radius of its inscribed circle)

Radius of base of equilateral triangle: root number is 3.

Using the volume formulas of cylinder and cone respectively, the volume ratio of circumscribed cylinder and circumscribed equilateral cone is obtained.

2:3

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