Cube - problems

  1. Cube cut
    cut_cube In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
  2. Perfect cubes
    cubes3_7 Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube?
  3. The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  4. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  5. Area to volume
    two_cubes_2 If the surface area of a cube is 486, find its volume.
  6. Cube
    cube_diagonals_3 The sum of all cube edges is 30cm. Find the surface area of the cube.
  7. Cube in a sphere
    cube_in_sphere The cube is inscribed in a sphere with volume 8818 cm3. Determine the length of the edges of a cube.
  8. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
  9. Transforming cuboid
    cube Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
  10. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 33 km.
  11. Tereza
    cube The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
  12. Prism
    3b_hranol Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
  13. Cube zoom
    krychle_1 How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
  14. Lathe
    soustruh From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
  15. Cube
    1cube Calculate the surface cube with edge 11 dm.
  16. Cube - angles
    cube_diagonal_1 Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
  17. Prism
    cuboid_2 Three cubes are glued into prism, sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube?
  18. Cube
    kocka_rubik The cube weighs 24 kg. How weight is cube of the same material, if its dimensions are 2-times smaller?
  19. Cube in ball
    sphere2 Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
  20. Hole
    cube_w_hole In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?

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