Cube - math word problems

  1. 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.
  2. The largest
    cylinder_in_cube The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
  3. The edge of a cube
    cubes How much does the edge of a cube of 54.9 cm3 measure?
  4. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  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. Water container
    cubes2 The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
  7. 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?
  8. Sum of the edges
    cube_shield The sum of the lengths of all edges of the cube is 72 cm. How many cm2 of colored paper are we going to use for sticking?
  9. 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?
  10. 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.
  11. Surface area of a cube
    cube_shield What is the surface area of a cube that has an edge of 3.5?
  12. Cube construction
    222cube A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
  13. Inscribed circle
    Cube_with_inscribed_sphere A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
  14. 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.
  15. Wooden container
    cube_shield The cube-shaped wooden container should be covered with a metal sheet inside. The outer edge of the container is 54cm. The wall thickness is 25 mm. The container has no lid. Calculate. How many sheets will be needed to cover it?
  16. Seat
    cubes3 How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
  17. Two cubes
    cubes2 The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
  18. 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?
  19. 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?
  20. Cube root
    cubes_27 For 13, Sam wrote 2891 instead of the correct cube number. By how much was he wrong?

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