Space diagonal + Pythagorean theorem - math problems

Space diagonal (also interior diagonal or body diagonal) of a polyhedron (i.e. prism, cube or rectangular cuboid) is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other.

  1. Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  2. 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.
  3. 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
  4. 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
  5. 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
  6. 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.
  7. Height of the room
    space_diagonal Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
  8. Tangent spheres
    tangent_spheres A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor an
  9. Cuboidal room
    Cuboid_simple_1 Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
  10. Find diagonal
    diagonal_3 Find diagonal of cuboid with length=20m width=25m height=150m
  11. Cube diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  12. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  13. Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  14. Body diagonal
    krychle_12 Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
  15. Deviation of the lines
    kvadr_1 Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
  16. Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  17. Solid cuboid
    cuboid_18 A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
  18. A box
    cuboid_15 A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
  19. Cube cut
    rezy The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
  20. Body diagonal - cube
    cube_shield Calculate the surface and cube volume with body diagonal 15 cm long.

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Pythagorean theorem is the base for the right triangle calculator. See also more information on Wikipedia.