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

Correct result:

V =  35.37 cm3

Solution:

u=6.1 cm a=3.2 cm b=2.4 cm  u=a2+b2+c2  c=u2a2b2=6.123.222.424.6054 cm  V=a b c=3.2 2.4 4.6054=35.37 cm3u=6.1 \ \text{cm} \ \\ a=3.2 \ \text{cm} \ \\ b=2.4 \ \text{cm} \ \\ \ \\ u=\sqrt{ a^2+b^2+c^2 } \ \\ \ \\ c=\sqrt{ u^2-a^2-b^2 }=\sqrt{ 6.1^2-3.2^2-2.4^2 } \doteq 4.6054 \ \text{cm} \ \\ \ \\ V=a \cdot \ b \cdot \ c=3.2 \cdot \ 2.4 \cdot \ 4.6054=35.37 \ \text{cm}^3



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Cuboid easy
    cuboid_11 The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
  • Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  • Concrete block
    abc 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.
  • Wall and body diagonals
    cube_diagonals The block/cuboid has dimensions a = 4cm, b = 3cm and c = 12cm. Calculates the length of the wall and body diagonals.
  • Height of the cuboid
    diagonal_rectangular_prism 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?
  • A box
    cuboid_15 A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
  • Triangular prism
    hranol_5 The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
  • Cuboid face diagonals
    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.
  • Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  • Find diagonal
    diagonal_3 Find diagonal of cuboid with length=20m width=25m height=150m
  • Height of the room
    space_diagonal Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
  • Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  • A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?