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. Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference. What is the volume of the cylinder in terms of its circumference, c?
  2. Surface of the cylinder
    valec_1 Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm
  3. Cuboid face diagonals
    face_diagonals The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
  4. Body diagonal
    kvadr_diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
  5. Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  6. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
  7. Wall and body diagonals
    diagonals_prism Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
  8. Alien ship
    cube_in_sphere The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the larges
  9. The cylinder 2
    cylinder Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
  10. Space diagonal
    cube_diagonals The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
  11. Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
  12. Axial section
    cone2 Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
  13. Cuboid
    cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
  14. Tetrahedral pyramid
    jehlanctyrboky What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
  15. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
  16. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  17. Cube diagonal
    cube_diagonal Determine the length of the cube diagonal with edge 75 mm.
  18. Tereza
    cube The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
  19. Logs
    gulatina Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
  20. Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.

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

To this e-mail address, we will reply solution; 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.