Cube + body volume - math problems

  1. Kostka
    sphere_in_cube Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
  2. Two rectangular boxes
    cuboid_2 Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
  3. The largest
    cylinder_in_cube The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
  4. The edge of a cube
    cubes How much does the edge of a cube of 54.9 cm3 measure?
  5. Surface of the cube
    cubes3 Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
  6. Nádoba
    cube_sphere_in Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby?
  7. A plasticine
    cubes3 Jožko modeled from plasticine. He used 27g of plasticine to model a 3 cm long cube. How many grams of plasticine will it need to mold cubes with an edge of 6cm?
  8. Length of the edge
    cube_shield Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
  9. Space diagonal
    cube_diagonals The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
  10. Cube into cylinder
    cube_sphere_in If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
  11. The cube
    cubes_28 The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?
  12. Cube surface and volume
    cube_diagonals_5 The surface of the cube is 500 cm2, how much cm3 will be its volume?
  13. The number
    cubes3_9 The number of 1 cm cubes required to make 4 cm cube is?
  14. Calculate 3
    cube_sphere_in_1 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
  15. 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.
  16. The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  17. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  18. Area to volume
    two_cubes_2 If the surface area of a cube is 486, find its volume.
  19. Bricks pyramid
    The_Great_Pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
  20. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.

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