1. It is easy to know that the distance between the center of the circle and the vertex and the distance between the center of the circle and a bottom surface are 3: 1 (which can be obtained by volume ratio), so the distance between the center of the circle and the bottom surface is 1/3. According to Pythagorean theorem, it is known that the radius of the circumscribed circle of a face of a regular triangular pyramid is (2√2)/3, so the face of a regular triangular pyramid is a triangle.

2. The radius of the bottom is √S/π, and the lateral area of the cylinder is (2r) 2 = 4s/π.

3. Let three sides be A, B and C, then 0.5ab=S 1.

0.5 BC =S2

0.5 AC =S3

The volume of the triangular pyramid is 1/3 *abc=2/3, and there are 2*S 1, S2.S3.

4.D

5.A