Body diagonal

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

Correct answer:

V =  81189.8816 dm³

Step-by-step explanation:

$$\begin{gathered} u=75\text{ dm } \\ a=u\mathrm{/}\sqrt{3}=75\mathrm{/}\sqrt{3}=25\sqrt{3}\text{ dm}\doteq 43.3013\text{ dm } \\ V=a^3=43.3013^3=81189.8816{\text{dm}}^3=8.119\cdot 10^4{\text{dm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Cube diagonals
  Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³.
• Body diagonal
  Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
• 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.
• Cube diagonals
  The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
• 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
  The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
• Body diagonal
  Calculate the length of the body diagonal of the 6cm cube.
• Cube wall
  Calculate the cube's diagonal if you know that one wall's surface is equal to 36 centimeters square. Please also calculate its volume.
• Cube wall
  The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube.
• Cube in a sphere
  The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube.
• Cube diagonal
  Determine the length of the cube diagonal with edge 37 mm.
• 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,
• Floating barrel
  Barrel (cylinder shape) floats on water, top of the barrel is 8 dm above water, and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
• Body diagonal
  Find the cube surface if its body diagonal has a size of 6 cm.
• Cube 7
  Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
• 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