What is the volume of a regular triangular pyramid if its four vertices are on a sphere of radius 1, and the three vertices of its bottom are on a big circle of the sphere

What is the volume of a regular triangular pyramid if its four vertices are on a sphere of radius 1, and the three vertices of its bottom are on a big circle of the sphere

According to the symmetry, we can see that the height of the triangular pyramid is the line between the vertex and the center of the ball, so the height is 1, obviously the edge length is √ 2, then the bottom area is s = √ 3 * (√ 2) ^ 2 / 4 = √ 3 / 2
The volume is v = SH / 3 = √ 3 / 6

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