If the five vertices of the pyramid p-abcd are on the same sphere, and the bottom surface is a square with side length 4, PA is perpendicular to ABCD, PA = 2, then the surface area of the sphere can be obtained

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• 1. 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
• 2. If the four vertices of an equilateral pyramid are on a sphere of radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the equilateral pyramid is The answer to this question is that the bottom is an equilateral triangle and the radius of the ball is 1 The side length of the bottom surface is √ 3, The bottom area is 3 √ 3 / 4, ∴V=1／3×3√3／4×1=√3／4． I want to know why the side length of the bottom is root three. Is there any formula
• 3. 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___ ．
• 4. 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___ ．
• 5. Let vertex a (1,1) B (5,3) C (4,5) be the vertex of △ ABC, find the coordinates of the center of gravity of △ ABC (1), the area of △ ABC passing through point a, etc (2) A linear equation that bisects the area of △ ABC through point a
• 6. For the vertex of △ ABC, find (1) the coordinate of the center of gravity of △ ABC, (2) the linear equation of the area of △ ABC through point a
• 7. It is known that the side edge length of p-abc is 10cm, and the side area is 144cm. The side length and height of p-abc are calculated
• 8. If the side length of the bottom is a, then the total area of the pyramid is a______ ．
• 9. If the side length of the bottom is a and the sides are right triangles, calculate the side area It's a regular pyramid
• 10. If the sides of a regular triangular pyramid are right triangles and the length of its bottom side is a, then its total area is?
• 11. Each vertex of the cuboid abcd-a1b1c1d1 is on the sphere of the sphere o with the volume of 32 / 3 Pai, where Aa1 = 2, then the volume of the pyramid o-abcd is smaller The maximum value is
• 12. Given three vertices a, B, C of △ ABC and a point P in the plane, if the vector PA + Pb + PC = AB, then the positional relationship between point P and △ ABC is? The relationship between PA and PC is obtained
• 13. If we know three vertices a, B, C of ⊿ ABC and a point P in the plane, satisfying PA + Pb + PC = 0, then point P is () A. Center of gravity
• 14. In the isosceles triangle ABC, ab = AC = 6, P is a point on BC, and PA = 4, then what is the value of Pb × PC?
• 15. P is a point in the equilateral triangle ABC. If the distance from P to three sides is equal, then PA = Pb = PC Please prove this proposition,
• 16. In tetrahedral PABC, PA, Pb and PC are perpendicular. It is proved that △ ABC is an acute triangle In tetrahedral PABC, PA, Pb and PC are perpendicular. It is proved that ① △ ABC is an acute triangle. ② the square of s △ ABC = the square of s △ PBC + the square of s △ PAB + the square of s △ PCA
• 17. It is known that △ ABC ∽ def, the lengths of three sides of △ ABC are radical 2, radical 14, 2, and the lengths of two sides of △ def are 1 and radical 7 respectively, so the third side of △ def can be obtained To solve the process
• 18. It is known that the three sides of △ ABC are a = 2, radical 5, B = radical 13 and C = radical 61. Try to find the area of △ ABC Associative figure
• 19. How to set up a rectangular coordinate system for a pyramid whose base side length is 5, root 2, and side edge length is 13?
• 20. The bottom of the Mitsubishi cone is an equilateral triangle with side length a, and the length of the two sides is (root number 13) a / 2. Try to find the value range of the third side length