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. Three cubes
    cubes3 The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
  2. Excavation
    vykop_1 Excavation for the base of the cottage 4.5 m x 3.24 m x 60 cm. The excavated soil will increase its volume by one-quarter. Calculate the volume of excavated soil.
  3. Container
    valec2_5 The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
  4. Cardboard
    cuboid_14 How many m2 of cardboard are needed to make the cuboid with dimensions 40 cm 60 cm and 20 cm?
  5. Sheet of paper
    cubes2_3 Is the sheet of paper measuring 18 and 25 cm enough for taping 9 cm cubes with an edge? (1 = yes, 0 = no)
  6. Cube surface area
    cubes2_2 The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased.
  7. Two cuboids
    cuboid_13 Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
  8. Clay
    lopatka How many cubic centimeters of clay is in a pit of dimensions 4 m x 3 m x 3 m?
  9. Cuboid
    cuboid_12 Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
  10. Surface of cuboid
    kvader11_9 Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
  11. Volume of cube
    cubes2_1 Solve the volume of a cube with width 26cm .
  12. 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.
  13. Cuboid walls
    cuboid_9 Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
  14. Cuboid height
    kvader11_8 What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
  15. Hollow sphere
    sphere2 The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
  16. Metal pyramid
    jehlan_5 Find the weight of a regular quadrilateral pyramid with a 5 cm length and 6,5 cm body height is made from material with density g/cm3.
  17. Water flow
    pipe2 How much water flow in pipe with a diameter of 16 cm in 1 hour if the water velocity is 2.5 m/s?
  18. Cremons
    wagon The freight wagon is shaped like cuboid 21m and 3.5m and 4.2m How many cremons can be loaded if one is a cube with an edge length of 7 cm?
  19. Stones in aquarium
    akvarko_7 In an aquarium with a length 2 m; width 1.5 m and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m3 into the aquarium without water being poured out?
  20. Flowerbed
    zahon_5 The flowerbed has a length 3500mm and a width 1400mm. How many foil is needed to covers the flowerbed? How many m2 of foil was consumed for its production (add 10% of the material to the joint and waste)? How many liters of air is inside the enclosure? (

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.