Ask Question
1 January, 22:42

10m^2 of tiles cover a pool, the pool is shaped as a square, so all four edges are the same, and the depth is constant but not equal to the size of the side. what is the maximum volume?

+5
Answers (1)
  1. 2 January, 02:01
    0
    Assume:

    Size of sides = x m

    Depth of the pool = y m

    Therefore, surface area = x^2+4xy = 10 m^2

    Then, y = (10-x^2) / (4x)

    Now,

    Volume (V) = x^2*y = x^2*y = x^2 (10-x^2) / 4x = (10x-x^3) / 4 = 1/4 (10x-x^3)

    For maximum volume, first derivative of volume function is equal to zero.

    That is,

    dV/dx = 0 = 1/4 (10-3x^2)

    Then,

    1/4 (10-3x^2) = 0

    10-3x^2 = 0

    3x^2=10

    x = sqrt (10/3) = 1.826 m

    And

    y = (10-1.826^2) / (4*1.826) = 0.913 m

    Therefore,

    V = 1.826^2*0.913 = 3.044 m^3
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “10m^2 of tiles cover a pool, the pool is shaped as a square, so all four edges are the same, and the depth is constant but not equal to the ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers