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. Cube in a sphere The cube is inscribed in a sphere with volume 3234 cm3. Determine the length of the edges of a cube.
2. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
3. Cube diagonal Determine length of the cube diagonal with edge 75 mm.
4. Forces In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
5. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
6. Prism The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
7. Two balls Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
8. Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
9. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
10. Box Calculate the angle between box base 9 x 14 and body diagonal length 18.
11. Cuboid Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
12. Nice prism Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
13. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
14. Tetrahedral pyramid It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
15. Sphere vs cube How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
16. Body diagonal 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,
17. 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?
18. Cube wall The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
19. Concrete block Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
20. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.

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