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.)