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. Surface of the cylinder
    cylinder_3 Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
  2. Volume and surface
    image001(1) Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
  3. Tin with oil
    konzerva Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
  4. The cylindrical container
    cylinder_1 The container has a cylindrical shape the base diameter 0.8 meters has a content area of the base is equal to the content area of the shell. How many full liters of water can be poured maximally into the container?
  5. Fire tank
    pool_3 How deep is the fire tank with the dimensions of the bottom 7m and 12m, when filled with 420 m3 of water?
  6. Juice box 2
    pfanner-ananas Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of th
  7. Max - cone
    cone_4 From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste.
  8. Water level
    hladina.JPG How high reaches the water in the cylindrical barell with a diameter of 12 cm if there is a liter of water? Express in cm with an accuracy of 1 decimal place.
  9. Barrel 3
    sud-s-vodou Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
  10. Truck of milk
    daf How many hectoliters of ,,the box" milk fit in the truck, ake cargo size area is 2.8 m x 3 m x 17 m? A liter of milk in a box measuring 12 cm x 7 cm x 20 cm.
  11. Garden pool
    basen_1 Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool?
  12. Water
    storm_1 On the lawn which has area 914 m2 rained 3 mm of water. How many liters of water rained?
  13. Cuboid
    Cuboid_BBC How many times will increase the volume of a cuboid, if one dimension is twice larger, second dimension three times larger and third dimension four times lower?
  14. Greenhouse
    foliovnik Garden plastic greenhouse is shaped half cylinder with a diameter of 6 m and base length 20 m. At least how many m2 of plastic is need to its cover?
  15. Bottles of juice
    juice_cones How many 2-liter bottles of juice need to buy if you want to transfer juice to 50 pitchers rotary cone shape with a diameter of 24 cm and base side length of 1.5 dm.
  16. Wood
    timber Wood contains 12% water. 1 m3 of wood weighs 650 kg. How many liters of water it contains?
  17. Weight of air
    weighting What is the weight of air in the living room measuring width 10 m length 3 m and height 3.3 m? Air density is ρ = 1.2 kg/m3.
  18. Cylinder diameter
    valec.JPG The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?
  19. Cuboid - edges
    kvadr The sum of all edges cuboid are 8 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid.
  20. Cuprum
    plusminus From 1600 mm long sheet of copper plate 2 mm thickness we have separated over the whole length the belt weighing 6000 g. Calculate belt width if 1 dm3 copper weighs 8.9 kg.

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.