Volume + third power - math problems

  1. Magnified cube
    cube_in_sphere If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
  2. Cuboid and ratio
    cuboid_2 Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
  3. Wall thickness
    sphere_Nickel The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
  4. The ball
    sphere4 The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
  5. 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.
  6. Alien ship
    cube_in_sphere The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
  7. Right circular cone
    cut-cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
  8. 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?
  9. Calculate 3
    cube_sphere_in_1 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
  10. Volume of ball
    ball1_5 Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
  11. The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  12. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  13. Edges or sides
    cube_shield_4 Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
  14. Seawater
    ice_cubes Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
  15. Minimum surface
    cuboid_20 Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
  16. Pyramid cut
    ihlan_rez We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
  17. No smoke
    no_smoking Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with the cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. The regular cigarette contains 0.8 mg of nicotine. How much nicotine would a gian
  18. Cube edges
    cubes3_3 If the edge length of the cube increases by 50%, how does the volume of this cube increase?
  19. Volume and body diagonal
    kvader11_11 Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
  20. Cuboid edges in ratio
    cuboid_11 Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.

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