# Space diagonal - math word 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.- Kostka

Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule? - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - Quadrilateral prism

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°. - Cuboid 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. - Body 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 - Faces diagonals

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 - 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 - Space diagonal

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

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? - Prism diagonal

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? - 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 - 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 - Find diagonal

Find diagonal of cuboid with length=20m width=25m height=150m - Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm^{3}. - Body diagonal

Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal. - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm. - Deviation of the lines

Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste. - Angle of diagonal

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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