Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

  1. Water
    rain In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water?
  2. Cuboid - simple
    cuboid_6 Calculate the surface area and volume of a cuboid if a = 8 cm, b = 14 cm and c = 6 cm.
  3. Wood planks
    fosny 1 m3 of wood planks costs 179 EUR. How much will I pay for 11 planks measuring 6 cm, 10 cm and 6 m?
  4. Concrete pillar
    hranol_4bok_pravidelny How many m³ of concrete is needed for the construction of the pillar shape of a regular tetrahedral prism, when a = 60 cm and the height of the pillar is 2 meters?
  5. Cube 3
    krychle_2 How many times will increase the volume of a cube if we double the length of its edge?
  6. Cube 2
    krychle_1 How many times will increase if the surface area of the cube if we triple length of its edge?
  7. Cuboids in cube
    shapes How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
  8. Cube
    krychle How many times increases the surface area of a cube with edge 23.4 cm if the length of the edge doubled?
  9. Stone
    kamen When Peter threw stone in a box of water he discovered that the water level has risen by 6 cm. The box has a cuboid shape, the bottom has dimensions of 24 cm and 14 cm, height is 40 cm. What volume has a stone?
  10. Water pool
    water What water level is in the pool shaped cuboid with bottom dimensions of 25 m and 10 meters, when is 3750hl water in the pool.
  11. Snow
    sneh_lopatovanie Snow fell overnight layer of thickness 19 cm. In the morning I had to clear a path 69 m long and one meter wide. How many cubic meters of snow I clear? How many kilos was it? (1 m3 fresh snow weighs 350 kg)
  12. Concrete box
    truhlik The concrete box with walls thick 5 cm has the following external dimensions: length 1.4 m, width 38 cm and height 42 cm. How many liters of soil can fit if I fill it to the brim?
  13. Soil pit
    tatra Workers dug a pit cube with edge 2.5 meters. How many cars shall remove soil if the car suddenly take 4m³ of soil?
  14. Painter
    painting_1 How many euros we will pay for repainting the room shaped cuboid with a length of 4.5 meters, width of 2.5 meters and a height of 3 meters, if for 1 m2 with paint we pay € 1.5?
  15. Milimeters
    plavani The pool is 6 meters long, 3 meters wide and the water in it is filled with water to a height 1.7 m. When John jumped into it and completely submerged, the level has risen by 5.4 mm. How much weight John when we know that one liter of the human body weigh
  16. Water lake
    jezirko The length of the lake water is 8 meters width 7 meters and depth 120 centimeters. How many liters of water can fit into the water lake?
  17. Cubes - diff
    cube_2 Second cubes edge is 2 cm longer than the edge of the first cube. Volume difference blocks is 728 cm3. Calculate the sizes of the edges of the two dice.
  18. Two boxes-cubes
    3-kostky Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
  19. Brass tube
    Ms_trubka The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
  20. Sphere area
    sphere A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

See also more information on Wikipedia.