If the four vertices of a regular triangular pyramid are on a sphere with radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the regular triangular pyramid is___ ．

If the four vertices of a regular triangular pyramid are on a sphere with radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the regular triangular pyramid is___ ．

The four vertices of a regular triangular pyramid are all on a sphere with radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, so the center of the sphere is the center of the triangle on the bottom surface. Let the radius of the sphere be 1, so the side length of the triangle on the bottom surface is a, 23 × 32A = 1, a = 3. The volume of the regular triangular pyramid is 13 × 34 × (3) 2 × 1 = 34, so the answer is: 34