Stereometry - examples

  1. Railway wagon
    cargo The railway wagon holds 75 m3 load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons?
  2. Cube
    1cube Calculate the surface cube with edge 25 mm.
  3. Pool
    swimming-pool The swimming pool is 6 m wide and 14 m long and 185 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
  4. Transforming cuboid
    cube Cuboid with dimensions 12 cm, 20 and 8 cm is converted into a cube with the same volume. What is its edge length?
  5. Hole
    vykop They fill shape hole with dimensions 2.5 m, 18 m, 11.8 m with 260 m3 of soil. How many percent it fill up?
  6. Lathe
    soustruh From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
  7. Cubes
    rubik_cube Cube, which consists of 27 small cubes with edge 3 dm has volume:
  8. Rotating cone
    cone Calculate volume of a rotating cone with base radius r=7 cm and height h=17 cm.
  9. Sphere growth
    sphere How many times grow volume of sphere if radius rises 3×?
  10. Air mass
    airbaloon What is the weight of the air in a classroom with dimensions 5 m × 2 m × 3.1 m ? The air density is 1.293 kg/m3.
  11. Pipes
    water_pipe Water pipe has a cross-section 1939 cm2. An hour has passed 567 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 14 hours if water flow same speed?
  12. Barrel of oil
    dieselbarrel Barrel of oil weighs 282 kg. When it mold 56% oil, weighed 138 kg. What is the mass of the empty barrel?
  13. Cylinder
    cyl_1 The cylinder-shaped container has 80 liters of water. The water reaches 45 cm height. How many liters of water will be in a container if water level extend to a height 72 cm? Write the result in liters, write down only as a whole or decimal number.
  14. Cube wall
    kocka Surface of first cube wall his 361 cm2. Second cube area is 30% of the surface of the first cube. Determine the length of the edge of the second cube (x).
  15. Cube
    kocka_rubik The cube weighs 18 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
  16. Water
    cylinder_1 Into a full cylindrical tank high 2 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.3 m, 1.5 m. How many liters of water will come out?
  17. Fire tank
    pool_3 How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?
  18. Eiffel Tower
    eiffel_tower Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 4.8 kg?
  19. Volume from surface area
    cube_3 What is the volume of the cube whose surface area is 96 cm2?
  20. Tetrapack
    tetrapack How high should be the milk box in the shape of a prism with base dimensions 8 cm and 14.2 cm if its volume is 1 liter?

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