Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm.

Correct answer:

S =  72 cm²

Step-by-step explanation:

$$\begin{gathered} u=6 \\ a=u\mathrm{/}\sqrt{3}=6\mathrm{/}\sqrt{3}=2\sqrt{3}\doteq 3.4641 \\ S=6\cdot a^2=6\cdot 3.4641^2=72{\text{cm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Body diagonal - cube
  Calculate the surface and cube volume with body diagonal 15 cm long.
• 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.
• Space diagonal
  The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
• Center of the cube
  The Center of the cube has a distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube.
• Surface and volume - cube
  Find the surface and volume of a cube whose wall diagonal is 5 cm long.
• Body diagonal
  Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
• Cube wall
  The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
• Cube diagonals
  The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
• Nice prism
  Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
• Cube cut
  The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
• Space diagonal angles
  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.
• Body diagonal
  Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
• Body diagonal
  Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
• Body diagonal
  Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
• 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,
• 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?