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?

Correct result:

u =  6 cm

Solution:

V=a2 c=32 4⋅ a⋅ c=2 a2 2c=a 4c2 c=32 c3=8 c=83=2 a=2⋅ c=2⋅ 2=4 u=a2+a2+c2=42+42+22=6 cm

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Cuboid
    cuboid Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  • Solid cuboid
    cuboid_18 A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
  • Nice prism
    diagonal_rectangular_prism.JPG 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 diagonals
    cube_diagonals_4 Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
  • Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  • Prism X
    Cuboid_simple The prism with the edges of the lengths x cm, 2x cm, and 3x cm has volume 20250 cm3. What is the area of the surface of the prism?
  • Uboid volume
    cuboid Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
  • Cube diagonals
    krychlicka_1 Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
  • Cuboid diagonals
    kvadr_diagonal The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
  • Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  • Cube surfce2volume
    cube_shield Calculate the volume of the cube if its surface is 150 cm2.
  • The cube
    cube_in_sphere The cube has a surface of 600 cm2, what is its volume?
  • Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  • 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?
  • Body diagonal - cube
    cube_shield Calculate the surface and cube volume with body diagonal 15 cm long.
  • Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  • Surface area of the top
    cylinder_4 A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.