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?

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