# 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.

#### Number of examples found: 54

• Center of the cube Center of the cube has distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube.
• Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
• Height of the room 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?
• Wall and body diagonals Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
• Cuboid - volume, diagonals The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
• Body diagonal Find the cube surface if its body diagonal has a size of 6 cm.
• Cube cut The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
• Cuboidal room 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
• Kostka Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
• Box Calculate the angle between box base 9 x 14 and body diagonal length 18.
• Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
• Body diagonal Calculate the length of the body diagonal of the 6cm cube.
• Cuboid easy The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
• Find diagonal Find diagonal of cuboid with length=20m width=25m height=150m
• Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
• Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
• Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
• Cube diagonal Determine the length of the cube diagonal with edge 37 mm.
• Angle of the body diagonals Using vector dot product calculate the angle of the body diagonals of the cube.
• Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.

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