Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.

Result

a =  9 cm
u1 =  12.728 cm
u2 =  15.588 cm

Solution:

S1=81 cm2  a=S1=81=9 cmS_{1}=81 \ \text{cm}^2 \ \\ \ \\ a=\sqrt{ S_{1} }=\sqrt{ 81 }=9 \ \text{cm}
u12=a2+a2=2 a2 u1=2⋅ a=2⋅ 9≐9 2≐12.7279≐12.728 cmu_{1}^2=a^2 + a^2=2 \ a^2 \ \\ u_{1}=\sqrt{ 2 } \cdot \ a=\sqrt{ 2 } \cdot \ 9 \doteq 9 \ \sqrt{ 2 } \doteq 12.7279 \doteq 12.728 \ \text{cm}
u22=a2+a2+a2=3 a2 u2=3⋅ a=3⋅ 9≐9 3≐15.5885≐15.588 cmu_{2}^2=a^2 + a^2 + a^2=3 \ a^2 \ \\ u_{2}=\sqrt{ 3 } \cdot \ a=\sqrt{ 3 } \cdot \ 9 \doteq 9 \ \sqrt{ 3 } \doteq 15.5885 \doteq 15.588 \ \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!





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

Showing 1 comment:
#
Math student
very nice this calculator thnk

avatar









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

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Wall diagonal
    cube_6 Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
  2. Cube cut
    rezy The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
  3. Body diagonal
    diagonal_1 Calculate the length of the body diagonal of the 6cm cube.
  4. Body diagonal
    cubes3_1 Find the cube surface if its body diagonal has a size of 6 cm.
  5. Square diagonal
    square_diagonal Calculate the length of diagonal of the square with side a = 23 cm.
  6. Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  7. Tetrahedral pyramid
    jehlan_3 It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
  8. Park
    diamond_3 In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
  9. Satin
    diagonal_rectangle_3 Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
  10. Find diagonal
    diagonal_3 Find diagonal of cuboid with length=20m width=25m height=150m
  11. 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).
  12. Isosceles trapezoid
    lichobeznik_mo_z8_5 What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
  13. 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?
  14. 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?
  15. 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?
  16. 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)?
  17. Center traverse
    trianles It is true that the middle traverse bisects the triangle?