Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.

Result

a =  3 cm
u1 =  4.243 cm
u2 =  5.196 cm

Solution:

V=27 cm3 a=V3=273=3=3  cm V = 27 \ cm^3 \ \\ a = \sqrt[3]{ V} = \sqrt[3]{ 27 } = 3 = 3 \ \text{ cm }
u1=2⋅ a=2⋅ 3=3 2≐4.2426=4.243  cm u_{ 1 } = \sqrt{ 2 } \cdot \ a = \sqrt{ 2 } \cdot \ 3 = 3 \ \sqrt{ 2 } \doteq 4.2426 = 4.243 \ \text{ cm }
u2=3⋅ a=3⋅ 3=3 3≐5.1962=5.196  cm u_{ 2 } = \sqrt{ 3 } \cdot \ a = \sqrt{ 3 } \cdot \ 3 = 3 \ \sqrt{ 3 } \doteq 5.1962 = 5.196 \ \text{ cm }

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  2. Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  3. Wall diagonal
    cube_6 Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
  4. Center of the cube
    center_of_cube Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
  5. Body diagonal
    krychle_12 Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
  6. Cube diagonal
    cube_diagonal Determine the length of the cube diagonal with edge 37 mm.
  7. Cube in sphere
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
  8. Body diagonal
    cubes3_1 Find the cube surface if its body diagonal has a size of 6 cm.
  9. The volume 2
    cubes3_11 The volume of a cube is 27 cubic meters. Find the height of the cube.
  10. Cube corners
    polyhedra-truncated-cube From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body?
  11. Two diagonals
    rhombus-diagonals The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
  12. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  13. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  14. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  15. Square2
    square_2 Side of the square is a = 6.2 cm, how long is its diagonal?
  16. The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
  17. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?