An aquarium with a square base has no top. there is a metal frame. glass costs 10 dollars/m^2 and the frame costs 9 dollars/m. the volume is to be 20 m^3. express the total cost c in terms of the height h in meters. (hint: work out the cost of the glass and frame separately.)

The volume is given as V = Lwh = 20 m^3.
Since the base is a square then V = L²h = 20 m^3
Rearranging, we have L = √(20/h).

For the metal frame:
8√(20/h) + 4h ==> [8 is multiplied to √(20/h) because there are 8 sides measuring L, and 4 is multiplied to h because there are 4 sides that have measure h.]

9[8√(20/h) + 4h]
=72√(20/h) + 36h = Cost of metal frame

For the glass:
Area of one square base = L² = 20/h
Area of one rectangular side = h√(20/h) 
Area of 4 rectangular sides = 4h√(20/h) 

10[20/h + 4h√(20/h)] = Cost of glass

C = 72√(20/h) + 36h + 10[20/h + 4h√(20/h)] 

(take note, we did not multiply 10 to the terms because 10 dollars is per unit area and not unit length.)

C. expression because any expression or equation may contain more than one variable