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. Area to volume
    two_cubes_2 If the surface area of a cube is 486, find its volume.
  2. Cube
    cube_diagonals_3 The sum of all cube edges is 30cm. Find the surface area of the cube.
  3. Orlík hydroelectric plant
    1280px-Orlík_1 The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the p
  4. Bucket
    watertank_4 The bucket half filled with water weighs 5.55 kg, the full bucket weighs 9.85 kg. How much does the bucket weigh?
  5. TV transmitter
    praded The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
  6. Rectangular cuboid
    cuboid_1 The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
  7. Pool
    swimming-pool The swimming pool is 4 m wide and 9 m long and 158 cm deep. How many hectoliters of water is in it, if the water is 27 cm below its upper edge.
  8. Transforming cuboid
    cube Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
  9. Sphere
    1sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
  10. 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 2.4 kg?
  11. Pipes
    water_pipe Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
  12. Tanks
    hasici Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
  13. Gutter
    okap How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
  14. Bricks
    bricks_truck Brick has volume 2.2 dm3. How many bricks can drive truck with capacity 23 ton? The density of brick is 1.6 g/cm3.
  15. Barrel of oil
    dieselbarrel Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel?
  16. Cube zoom
    krychle_1 How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
  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. Lathe
    soustruh From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
  19. Rotation
    cone_1 Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
  20. Air mass
    airbaloon What is the weight of the air in a classroom with dimensions 10 m × 0 m × 2.5 m ? The air density is 1.293 kg/m3.

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