# math

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A water tank can be constructed with a metal top and two square ends that holds 16 cubic meter of water and requires 40 square meter of metal. find the dimensions of the water tank.

• math -

if the ends have side x, and the tank has height h,
x^2 h = 16
2x^2 + 4xh = 40
2x^2 + 4x(16/x^2) = 40
x^2 + 32/x = 20
x^3 - 20x + 32 = 0
(x-2)(x^2+2x-16) = 0
so, if x=2, the tank is 2x2x4

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