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. How much
    woord_1 How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
  2. Cuboid
    kvader11 The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
  3. Cube edges
    cubes3_3 If the edge length of the cube increases by 50%, how does the volume of this cube increase?
  4. Cylinder-shaped vase
    vaza_1 If the cylinder-shaped vase is filled with water up to 35 cm, it contains 1 liter of water. How much water will it contain if it is filled to a height of 45cm?
  5. Water tank
    nadrz_13 A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
  6. Cylindrical container
    valec2_6 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
  7. Cuboid
    cuboid_1 The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
  8. Pool
    swimming-pool The swimming pool is 4 m wide and 20 m long and 156 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
  9. Transforming cuboid
    cube Cuboid with dimensions 5 cm, 14 and 17 cm is converted into a cube with the same volume. What is its edge length?
  10. Sphere
    1sphere Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
  11. 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?
  12. Pipes
    water_pipe Water pipe has a cross-section 1420 cm2. An hour has passed 831 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 8 hours if water flow same speed?
  13. Tanks
    hasici Fire tank has cuboid shape with a rectangular floor measuring 14 m × 12.8 m. Water depth is 1.8 m. Water was pumped from the tank into barrels with a capacity of 4.4 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wri
  14. Gutter
    okap How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material.
  15. Bricks
    bricks_truck Brick has volume 2.2 dm3. How many bricks can drive truck with capacity 20 ton? The density of brick is 2 g/cm3.
  16. Barrel of oil
    dieselbarrel Barrel of oil weighs 238 kg. When it mold 20% oil, weighed 196 kg. What is the mass of the empty barrel?
  17. Sand pile
    sandpile_1 Auto sprinkled with sand to approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the sand c
  18. Cube zoom
    krychle_1 How many percent we increase volume and surface of cube, if we magnify its edge by 61%.
  19. Lathe
    soustruh From the cube of edge 52 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
  20. Rotation
    cone_1 Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.

Do you have interesting mathematical example that you can't solve it? Enter it and we can try to solve it.



To this e-mail address we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.



See also more information on Wikipedia.