Wall and body diagonals

The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.

Correct answer:

u₁ =  5 cm
u₂ =  12.3693 cm
u₃ =  12.6491 cm
d =  13 cm

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ b=3\text{ cm } \\ c=12\text{ cm } \\ {u}_1=\sqrt{a^2+b^2}=\sqrt{4^2+3^2}=5\text{ cm} \end{gathered}$$

$u_2=\sqrt{b^2+c^2}=\sqrt{3^2+12^2}=3\sqrt{17}=12.3693\text{ cm}$

$u_3=\sqrt{a^2+c^2}=\sqrt{4^2+12^2}=4\sqrt{10}=12.6491\text{ cm}$

$d=\sqrt{a^2+b^2+c^2}=\sqrt{4^2+3^2+12^2}=13\text{ cm}$

Try another example

Related math problems and questions:

• 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
  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
• Cuboid face diagonals
  The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
• Cuboid easy
  The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
• Body diagonal
  Find the length of the body diagonal of a cuboid with edges lengths of 16 cm, 7 cm, and 4 cm.
• Concrete block
  Determine the volume of the concrete block whose one edge of the base has a length of 3 meters, body diagonal is 13 meters, and its height is 12 meters.
• Height of the cuboid
  Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?
• Diagonals of a prism
  The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base.
• 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?
• Prism 4 sides
  The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
• Cuboid diagonals
  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.
• 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,
• Wall and body diagonals
  Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
• 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.
• Cube diagonals
  The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
• Ratio of edges
  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.
• Distance of lines
  Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm