Solid geometry, stereometry - page 15

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. Cuboid - Vab
    cuboid_3 Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters.
  2. Cube, cuboid, and sphere
    cubes3_8 Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
  3. Equilateral cylinder
    sphere_in_cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
  4. Volume and body diagonal
    kvader11_11 Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
  5. The tank
    nadrz_15 The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?
  6. Cube into sphere
    cube_sphere_in The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  7. Circular pool
    b1 The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
  8. Big cube
    cubes_23 Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long.
  9. 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?
  10. 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.
  11. Cube edges
    cube_shield_3 The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
  12. 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.
  13. 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.
  14. Rainfall
    rain_6 A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
  15. Cube edges
    cubes3_3 If the edge length of the cube increases by 50%, how does the volume of this cube increase?
  16. Basen
    bazen_9 How many square meters of tiles we need to tile the walls and floor of the pool 15 meters long, six meters wide and two meters?deep
  17. Rain
    rain_8 It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
  18. Inscribed
    koule_krychle_1 Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
  19. 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?
  20. Hectoliters
    sudy_4 How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?

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