Space diagonal + right triangle - 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.

Number of problems found: 56

  • Space diagonal angles
    kvadr_diagonal Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
  • Body diagonal
    cuboid Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
  • Quadrilateral prism
    hranol The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
  • Distance of points
    jehlan_4b_obdelnik_1 A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
  • Regular hexagonal prism
    hexagon_prism2 Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
  • Wall and body diagonals
    cube_diagonals The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
  • Height of the cuboid
    diagonal_rectangular_prism Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • Quadrilateral prism
    hranol4sreg Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°.
  • 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
  • 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
  • Find diagonal
    diagonal_3 Find diagonal of cuboid with length=20m width=25m height=150m
  • Cuboid face diagonals
    face_diagonals_1_1 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.
  • 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 and
  • Body diagonal
    diagonal_1 Calculate the length of the body diagonal of the 6cm cube.
  • 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.
  • 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?
  • 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=1.3, y=1, z=1.2
  • Body diagonal - cube
    cube_shield Calculate the surface and cube volume with body diagonal 15 cm long.
  • 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

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See also our right triangle calculator. See also more information on Wikipedia.