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,

Correct answer:

u₁ =  8.0131 cm
h =  4.0976 cm

Step-by-step explanation:

$$\begin{gathered} a=7\text{ cm } \\ b=3.9\text{ cm } \\ u=9\text{ cm } \\ {u}_1=\sqrt{a^2+b^2}=\sqrt{7^2+3.9^2}=8.0131\text{ cm} \end{gathered}$$

$h=\sqrt{u^2-u_1^2}=\sqrt{9^2-8.0131^2}=4.0976\text{ cm}$

Try another example

Related math problems and questions:

• 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?
• 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
• Body diagonal
  Find the length of the body diagonal of a cuboid with lengths of 16 cm, 7 cm, and 4 cm.
• 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.
• 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.
• Prism - box
  The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.
• Body diagonal - cube
  Calculate the surface and cube volume with body diagonal 15 cm long.
• 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?
• Isosceles + prism
  Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm length of 3.7 cm
• Cuboid
  Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
• 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.
• 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.
• Body diagonal
  Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
• 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.
• Concrete block
  Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
• Quadrilateral prism
  The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
• 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.