Body diagonal

The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

Correct result:

u =  6 cm

Solution:

V=a2 c=32 4⋅ a⋅ c=2 a2 2c=a 4c2 c=32 c3=8 c=83=2 a=2⋅ c=2⋅ 2=4 u=a2+a2+c2=42+42+22=6 cmV=a^2 \ c=32 \ \\ 4 \cdot \ a \cdot \ c=2 \ a^2 \ \\ 2c=a \ \\ 4c^2 \ c=32 \ \\ c^3=8 \ \\ c=\sqrt[3]{ 8 }=2 \ \\ a=2 \cdot \ c=2 \cdot \ 2=4 \ \\ u=\sqrt{ a^2+a^2+c^2 }=\sqrt{ 4^2+4^2+2^2 }=6 \ \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
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.

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:

  • Water reservoir
    water_tower The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.
  • Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  • Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
  • Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  • Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  • 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.
  • Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  • Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  • Linsys2
    linear_eq_3 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
  • Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  • Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  • GP - three members
    progression_ao The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c
  • Geometric seq
    eq222_1 Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
  • Solve equation
    hrusky_2 solve equation: ?
  • Reciprocal value
    fx How do I calculate a number x that is 9 greater than its reciprocal (1/x)?
  • Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160
  • Warehouses
    silo_3 In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?