Let the area of the axial section of a cone be root 3, and the radius of the bottom surface be 1

The area of the axial section of the cone is root sign 3, the radius of the bottom surface is 1, the height is 2 * root sign 3 / 2 = root sign 3, and the bottom area is π (R ^ 2) = π
The volume is radical 3 * π / 3 = (π radical 3) / 3

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1. 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;
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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？、
8. 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?
9. In quadrilateral ABCD,
10. 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___ ．
11. 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
12. 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______ ．
13. 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
14. 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___ ．
15. 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?
16. 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___ ．
17. If the surface area of the cone is 15 π, then the center angle of the side view is 60 ° and the volume of the cone is? Let the generatrix be l and the bottom radius be r The lateral area is 60 × Pai × L Λ 2 / 360 = Pai × R × L L = 60R Why not?
18. Given that the generatrix of a cone is 5cm in length and 4cm in height, how to find the volume of the cone?
19. After cutting a 5 cm high cone along its height, the surface area increases by 10 square centimeters. What is the volume of this cone
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