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.

Number of problems found: 963

  • Aquarium height
    akvarko How high does the water in the aquarium reach, if there are 36 liters of water in it? The length of the aquarium is 60 cm and the width is 4 dm.
  • Cube surfce2volume
    cube_shield Calculate the volume of the cube if its surface is 150 cm2.
  • Spherical segment
    SphericalSegment_1000 Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
  • Cuboid edges
    cuboid_3 Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2: 3: 4 and the longest edge measures 10cm.
  • Cuboid to cube
    cube_shield_1 A cuboid with dimensions of 9 cm, 6 cm, and 4 cm has the same volume as a cube. Calculate the surface of this cube.
  • Surface and volume
    cuboid_2 Find the surface and volume of a cuboid whose dimensions are 1 m, 50 cm, and 6 dm.
  • The cube
    cube_shield_1 The cube has a surface area of 216 dm2. Calculate: a) the content of one wall, b) edge length, c) cube volume.
  • Copper Cu wire
    cu_wire Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
  • Eight
    sphere_in_cube Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls, or one big ball?
  • Magnified cube
    cube_in_sphere If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
  • AL wire
    vaha2 What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.
  • Runcated pyramid teapot
    komoly_jehlan The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
  • Identical cubes
    cubes3 From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?
  • Volume and surface area
    cuboid_2 Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
  • Net of a cube
    cube_shield This net can be folded to form a cube with a side length of 20 units. What is the surface area of the cube in square units?
  • Water tank
    nadrz 300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach?
  • Oak trunk
    stromy Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.
  • Cone from cube
    cones The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3
  • Rain
    rain Garden shape of a rectangle measuring 15 m and 20 m rained water up to 3 mm. How many liters of water rained on the garden?
  • Cannonballs
    sphere_Nickel Of the three cannonballs with a diameter of 16 cm, which landed in the castle courtyard during the battle, the castle blacksmith cast balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith c

Do you have an interesting mathematical word problem that you can't solve it? Submit a 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.