Cube diagonals

Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.

Correct result:

a =  3 cm
u1 =  4.243 cm
u2 =  5.196 cm

Solution:

V=27 cm3 a=V3=273=3 cm
u1=2⋅ a=2⋅ 3=3 2=4.243 cmu_{1}=\sqrt{ 2 } \cdot \ a=\sqrt{ 2 } \cdot \ 3=3 \ \sqrt{ 2 }=4.243 \ \text{cm}
u2=3⋅ a=3⋅ 3=3 3=5.196 cmu_{2}=\sqrt{ 3 } \cdot \ a=\sqrt{ 3 } \cdot \ 3=3 \ \sqrt{ 3 }=5.196 \ \text{cm}

Try another example


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!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric 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:

  • Body diagonal
    cube_diagonals_2 Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
  • Cube diagonals
    cube_diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
  • Center of the cube
    center_of_cube Center of the cube has distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube.
  • The edge of a cube
    cubes How much does the edge of a cube of 54.9 cm3 measure?
  • Square2
    square_2 Side of the square is a = 6.2 cm, how long is its diagonal?
  • Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  • 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).
  • Circle
    talesova On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
  • Spruce height
    stromcek_7 How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
  • 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?
  • Broken tree
    broken_tree The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
  • The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
  • 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)?
  • Oil rig
    oil_rig_tower Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
  • The double ladder
    dvojity_rebrik The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?
  • 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?
  • 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?