Space diagonal - 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: 72

  • 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.
  • 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.
  • 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?
  • Cube diagonal
    cube_diagonal Determine the length of the cube diagonal with edge 37 mm.
  • Body diagonal
    diagonal_1 Calculate the length of the body diagonal of the 6cm cube.
  • Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  • Cuboid diagonal
    cube_2 Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, c has dimensions in the ratio of 9:3:8. If you know that the diagonal wall AC is 86 cm, and the angle between AC and space diagonal AG is 25 degrees.
  • Body diagonal
    cubes3_1 Find the cube surface if its body diagonal has a size of 6 cm.
  • Find diagonal
    diagonal_3 Find the length of the diagonal of a cuboid with length=20m width=25m height=150m
  • Body diagonal
    krychle_12 Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
  • Cuboid
    cuboid Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  • Body diagonal - cube
    cube_shield Calculate the surface and cube volume with body diagonal 15 cm long.
  • Body diagonal
    space_diagonal Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
  • Volume and body diagonal
    kvader11_11 Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
  • Body diagonal
    kvader11_1 The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
  • Body diagonal
    cuboid Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
  • Box
    uhlopriecka Calculate the angle between box base 9 x 14 and body diagonal length 18.
  • Prism diagonal
    hranol222_2 The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
  • Body diagonal
    kvadr Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
  • Angle of diagonal
    hranol_9 The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.

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