Faces diagonals

If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid.

Solve for x=1.2, y=1.7, z=1.45

Result

V =  0.803

Solution:

x=1.2 y=1.7 z=1.45  x2=a2+b2 y2=b2+c2 z2=a2+c2  a2=x2−b2=x2−y2+c2=x2−y2+z2−a2 2a2=x2−y2+z2  a=x2−y2+z22=1.22−1.72+1.4522≐0.5712  ... b=x2+y2−z22=1.22+1.72−1.4522≐1.0553  ... c=−x2+y2+z22=−1.22+1.72+1.4522≐1.3328  V=a⋅ b⋅ c=0.5712⋅ 1.0553⋅ 1.3328≐0.8034=0.803x = 1.2 \ \\ y = 1.7 \ \\ z = 1.45 \ \\ \ \\ x^2 = a^2+b^2 \ \\ y^2 = b^2+c^2 \ \\ z^2 = a^2+c^2 \ \\ \ \\ a^2 = x^2 - b^2 = x^2-y^2+c^2 = x^2-y^2+z^2-a^2 \ \\ 2a^2 = x^2-y^2+z^2 \ \\ \ \\ a = \sqrt{ \dfrac{ x^2-y^2+z^2 }{ 2 } } = \sqrt{ \dfrac{ 1.2^2-1.7^2+1.45^2 }{ 2 } } \doteq 0.5712 \ \\ \ \\ ... \ \\ b = \sqrt{ \dfrac{ x^2+y^2-z^2 }{ 2 } } = \sqrt{ \dfrac{ 1.2^2+1.7^2-1.45^2 }{ 2 } } \doteq 1.0553 \ \\ \ \\ ... \ \\ c = \sqrt{ \dfrac{ -x^2+y^2+z^2 }{ 2 } } = \sqrt{ \dfrac{ -1.2^2+1.7^2+1.45^2 }{ 2 } } \doteq 1.3328 \ \\ \ \\ V = a \cdot \ b \cdot \ c = 0.5712 \cdot \ 1.0553 \cdot \ 1.3328 \doteq 0.8034 = 0.803

Try another example






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




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

Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

Next similar math problems:

  1. 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?
  2. Cuboidal room
    Cuboid_simple_1 Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
  3. Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  4. Three unknowns
    matrix_1 Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
  5. Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  6. Children
    children_3 The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
  7. Ball game
    lopta_3 Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
  8. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  9. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  10. Thunderstorm
    blesk The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
  11. Right angled triangle
    fun-triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
  12. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  13. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  14. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  15. Elimination method
    rovnice_1 Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
  16. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  17. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?