Regard it as a plan view, that bottom of a regular triangular prism is a regular triangle, and its inscribed circle is the maximum cross section of an inscribed sphere-that is, the radiu of the inscribed circle is equal to one third of the height of the regular triangle; The maximum cross section of the circumscribed sphere is related to the height of the regular triangular prism and the height of the bottom surface.

In this way, the relationship between the three is clarified, and the surface area ratio comes out.