Stereometry - problems

  1. Cone
    truncated_cone_1 Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
  2. Cube
    cube2 The sum of lengths of cube edges is 22 cm. What is its surface and volume?
  3. Reservoir + water
    cuboid_water Reservoir completely filled with water weighs 13 kg. After pouring off three quarters of the amount of water weights 4 kg. Calculate the weight and volume of the reservoir.
  4. Milk package
    madeta Milk is sold in a box with dimensions of 9.5 cm; 16.5 cm and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible.
  5. Cylinder - area
    valec The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
  6. Observatory
    kopula Observatory dome has the shape of a hemisphere with a diameter d = 7 m. Calculate the surface.
  7. Cone and cube
    shapes About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r?
  8. Cube corners
    2cube The wooden cube with edge 45 cm was cut in 4 corners of cube with edge 5 cm. How many cubes of edge 5 cm can be even cut?
  9. Iron fence
    fe One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
  10. Cube and water
    krychle_3 How many liters of water can fit into a cube with an edge length of 0.11 m?
  11. Cylinder - h2
    valec_1 Cylinder volume is 2.7 liters. Base area is 1 dm2. Calculate the height of the cylinder.
  12. Cuboid
    dodecagon The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?
  13. 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.
  14. 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?
  15. Cube edge
    cubes_9 Determine the edges of the cube when the surface is equal to 37.5 cm square.
  16. Freezer
    mraznicka The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, 30 cm. A layer of ice of 23 mm thick was formed on the inner walls (and on the opening) of the freezer. How many liters of water will drain if we dispose the freezer?
  17. Cube surface area
    cube_5 Wall of cube has content area 95 cm square. What is the surface of the cube?
  18. Cuboid
    cuboid_12 Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
  19. Volume of cube
    cubes2_1 Solve the volume of a cube with width 26cm .
  20. Cube
    1cube Calculate the surface cube with edge 29 dm.

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