Rectangle pool

Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.

Result

a =  4 m
c =  2 m

Solution:

V=32 a=b V=a2 c c=32/a2 S=a2+4ac=a2+4a(32/a2) S′=2a−128/a2 S′=0 2−128/a3=0 1−64/a3=0 a3=64 a=643=4 a=b=a=4=4  m V = 32 \ \\ a = b \ \\ V = a^2 \ c \ \\ c = 32/a^2 \ \\ S = a^2 +4ac = a^2 +4a (32/a^2) \ \\ S' = 2a-128/a^2 \ \\ S' = 0 \ \\ 2-128/a^3 = 0 \ \\ 1-64/a^3 = 0 \ \\ a^3 = 64 \ \\ a = \sqrt[3]{ 64 } = 4 \ \\ a=b = a = 4 = 4 \ \text { m }
c=32/a2=32/42=2=2  m c = 32/a^2 = 32/4^2 = 2 = 2 \ \text { m }

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? Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

  1. Swimming pool
    basen The pool shape of cuboid is 299 m3 full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second.
  2. 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.
  3. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  4. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  5. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  6. Equation with abs value
    abs_graph How many solutions has the equation ? in the real numbers?
  7. Quadrangular prism
    hranol_4 The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
  8. Quadratic equation
    Parabola_tangent Quadratic equation ? has roots x1 = -26 and x2 = -86. Calculate the coefficients b and c.
  9. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  10. Cuboid walls
    cuboid_19 If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
  11. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  12. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  13. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  14. Cuboid edges in ratio
    cuboid_11 Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
  15. Cinema 4
    cinema_2 In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?
  16. Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  17. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3