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. Tetrahedral prism - rhomboid base
    rhombus2_2 Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
  2. Regular quadrilateral pyramid
    pyramid_3 Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
  3. Hexagon rotation
    hexagnos A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
  4. Pool in litres
    bazen2_1 Pool has a width of 3.5 m length of 6 m and a height 1.60 meters. Calculate pool volume in liters.
  5. Painting a hut
    malovka_4 It is necessary to paint the exterior walls of hut whose layout is a rectangle of 6.16 m x 8.78 m wall height is 2.85 meters. Cottage has five rectangular windows; three have dimensions of 1.15 m x 1.32 m and two 0,45 m x 0.96 m. How many m2 is necessar
  6. Surface area of cylinder
    cylinder_cube Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
  7. Vintner
    wine How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number
  8. Surface and volume od cuboid
    kvader Content area of the square base of cuboid is Sp = 36 cm2 and its height 80 mm. Determine its surface area and volume.
  9. Tetrahedral pyramid
    jehlan_3 It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
  10. Horizontal Cylindrical Segment
    cylinder_horiz How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
  11. Triangular prism
    hranol_5 The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
  12. Cone
    r_h_cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
  13. Cuboid - edges
    kvader_abc The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
  14. Church roof
    veza_2 The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
  15. Hexagonal prism 2
    hranol6b The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
  16. The factory
    hutny material The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3?
  17. Cube walls
    krychle_6 Find the volume and surface area of the cube if the area of one wall is 40cm2.
  18. Quadrangular prism
    hranol_4 The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
  19. Pyramid in cube
    pyramid_in_cube In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.
  20. Sphere vs cube
    koule_krychle How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also more information on Wikipedia.