The axial section of a cone is an equilateral triangle with a side length of 2 root sign 3. The volume of the cone is equal to

3π………………

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1. It is known that the height of a cone is 6cm and the length of generatrix is 10cm. It is necessary to calculate the volume of the inscribed sphere and the surface area of the circumscribed sphere
2. If the volume of the cone is equal to that of the ball, and the radius of the bottom of the cone is twice that of the ball, then the ratio of the side area of the cone to the surface area of the ball is 0
3. If the height of the circumscribed cone of a sphere is three times the radius of the sphere, what is the ratio of the side area of the cone to the surface area of the sphere? It's a process. There is also a question: a cylindrical cylinder with a bottom radius of R is filled with an appropriate amount of water. If a solid iron ball with a radius of R is put in, the height of the water surface will just rise R. R/r？、
4. If the radius of the base area of the cone is √ 3 and the surface area of the inscribed sphere is 4 π, then the side area of the cone is?
5. In quadrilateral ABCD,
6. As shown in the figure, rectangular paper ABCD, ab = 2, ∠ ADB = 30 ° is folded along the diagonal BD (so that △ abd and △ EBD fall in the same plane), then the distance between a and E is___ ．
7. As shown in the figure, the rectangular piece of paper ABCD, ∠ ADB = 30 ° is folded along the diagonal BD (so that △ abd and triangle EBD fall in the same plane), when Ao = 2 cm, the length of ad is calculated
8. As shown in the figure, fold a rectangular piece of paper ABCD along AF to make point B fall at B ′. If ∠ ADB = 20 °, then how many degrees should ∠ BAF be to make ab ′‖ BD?
9. As shown in the figure, the rectangle ABCD rotates 90 ° clockwise around point a to the position of rectangle ab1c1d1. Ad = 10, calculate the area swept by edge BC
10. As shown in the figure, in the rectangular ABCD, AC is a diagonal, rotate ABCD clockwise 90 ° around point B to gbef position, h is the midpoint of eg, if AB = 6, BC = 8, then the length of segment ch is () A. 25B. 21C. 210D. 41
11. The length of the generatrix of the cone is 4, and the area of the cross-section triangle passing through the vertex is 4 root sign 3. Find the vertex angle of the cross-section triangle (2), the height of the cone is l, and the bottom radius is root sign 3 Find the maximum cross-sectional area of a cone vertex
12. If the height of the cone is 2 and the radius of the bottom is 2 root sign 3, the maximum cross-sectional area of the cone will be obtained
13. If the side area of a cone is 8 π square centimeter and its axis section is an equilateral triangle, the area of the axis section is () a 8 root sign 3 cm & # 178; B 4 root C 8 is 3 π CM & # 178; D 4 is 3 π CM & # 178;
14. Let the area of the axial section of a cone be root 3, and the radius of the bottom surface be 1
15. If the axial section of a cone (the section passing through the top and bottom diameter of the cone) is an equilateral triangle of area 3, then the total area of the cone is () A. 3πB. 33πC. 6πD. 9π
16. If the axial section of a cone is an equilateral triangle and its area is 3, then the side area of the cone is 3______ ．
17. The surface area of a cone is 7. The volume of a cone can be calculated by a sector of 60 degrees around the central angle of the circle
18. If the surface area of the cone is 15 π and the center angle of the side view is 60 °, then the volume of the cone is 15 π___ ．
19. If the surface area of the cone is 15 π and the center angle of the side view is 60 °, the volume of the cone will be smaller Detailed explanation: if the radius of the cone bottom is r, the perimeter of the cone bottom is 2 π R. if the center angle of the side view is 60 °, the arc length of the sector is 2 π R, and the radius of the sector is l, then 60 π L / 180 = 2 π R, l = 6R, the area of the sector is 2 π R × 6R / 2 = 6 π R & # 178; the surface area of the cone is 15 π = the bottom area + the area of the sector = π R & # 178; + 6 π R & # 178; = 7 π R & # 178;, R & # 178; = 15 / 7, r = √ 105 / 7, and the generatrix length of the cone is 6R, According to Pythagorean theorem, the height of the cone is √ 35r, and the volume of the cone is π R & # 178; × √ 35r / 3 = 25 π √ 3 / 7 π R & # 178; × √ 35r / 3 = 25, π √ 3 / 7 is wool?
20. If the surface area of the cone is 15 π and the center angle of the side view is 60 °, then the volume of the cone is 15 π___ ．