Question 657340
Let's start with the formula for volume:

{{{V = L * W * H}}}

We are told the ends are square, so 

{{{W = H}}} and {{{V = L * H * H = L * H^2}}}

We are also told that the volume is a constant 10,000 cubic inches, so we have

{{{10000 = L * H^2}}}

Solving for H:

{{{H = sqrt(10000/L)}}}

The area of the bottom is:

{{{A(bottom) = L * H = L * sqrt(10000/L) = sqrt(L^2*(10000/L)) = sqrt(10000*L) = 100*sqrt(L)}}}

The areas of the back and front are the same as the bottom:

{{{A(back) = 100*sqrt(L)}}}
{{{A(front) = 100*sqrt(L)}}}

And the total area of the two ends are:

{{{A(ends) = 2 * H*H = 2*sqrt(10000/L)*sqrt(10000/L) 2*(sqrt(10000/L))^2 = 2*(10000/L) = (20000/L)}}}

The cost for the bottom is 
{{{8.00*A(bottom) = 8.00*100*sqrt(L)}}}

The cost for the back is 
{{{5.00*A(back) = 5.00*100*sqrt(L)}}}

The cost for the front is
{{{0.70*A(front) = 0.70*100*sqrt(L)}}}

And finally, the cost for the two ends is

{{{0.70*A(ends) = 0.70*(20000/L)}}}

So the total cost of the aquarium is

{{{8.00*100*sqrt(L) + 5.00*100*sqrt(L) + 0.70*100*sqrt(L) + 0.70*(20000/L)}}}

Combining terms:

{{{1370*sqrt(L) + (14000/L)}}}