Question 1097462
<br>The first solution is not right....<br>
The aquarium has a square base of side length s and a height of h.  The volume is to be 20, so
{{{s^2h = 20}}}
{{{s^2 = 20/h}}}
{{{s = sqrt(20/h)}}}<br>
The glass required is for the base, area s^2, and four sides, each area s*h.  That total area is
{{{s^2 + 4sh = 20/h + 4h*sqrt(20/h)}}}
The cost of the glass is then
{{{10(20/h + 4h*sqrt(20/h))}}}<br>
The metal needed for the frame is 4 sides on top and 4 sides on bottom, each length s, and 4 vertical edges, each length h.  The total length of all the edges is
{{{8s + 4h = 8*sqrt(20/h)+4h}}}
and then the cost for the metal for the frame is
{{{10(8*sqrt(20/h)+4h)}}}<br>
Then an expression for the total cost in terms of the height h is<br>
{{{10(20/h + 4h*sqrt(20/h) + 8*sqrt(20/h)+4h)}}}