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. Prism
    prism The volume of tetrahedral prism is 2.43 m3. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.
  2. Lamp cone
    lampa Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
  3. 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.
  4. Cellar
    img1 Cellar for storing fruit has a rectangular base with sides 14 m and 7 meters. You should paint sidewall to 2 m. How m2 surface must be painted?
  5. Tent
    stan Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
  6. Hexagonal pyramid
    jehlan_6 Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
  7. 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.
  8. Cuboid - volume and areas
    cuboid_10 The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
  9. Bathroom
    koupelna How many CZK we pay for lining the perimeter walls of the bathroom with rectangular shape with dimensions 3.5 m and 4 m, high 1.5 m if 1 square m tile cost 300 CZK?
  10. Glass
    pohgar How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
  11. Area of the cone
    cone2_1 Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
  12. Chimney
    komin_melnik Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney.
  13. Hexa prism
    hexagon Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm.
  14. Square vs rectangle
    ctverec Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.
  15. Prism
    rhombic_prism Calculate the surface area and volume of a prism with a body height h = 10 cm and its base has shape of a rhomboid with sides a = 5.8 cm, b = 3 cm and the distance of its two longer sides is w = 2.4 cm.
  16. 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.
  17. Cube from sphere
    sphere_cube What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
  18. Rotating cone
    kuzel_3 Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
  19. The pot
    hrniec_1 Diameter of the pot 38 cm. The height is 30 cm. How many liters of water can fit in the pot?
  20. Rectangle pool
    basen_5 Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.

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