An aquarium with a square base has no top. there is a metal frame. glass costs 8 dollars/m^2 and the frame costs 7 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.)

Given that the volume of the aquarium is 20m^3.

Volume = Area of Base x height

Area of Base = Volume / height = 20/h

Given that the aquarium has a square base.

Area of square = l^2

Thus, the length of the base of the aquarium is

The frame is to cover 8 sides with the length equal to the length of the base and 4 sides with the length of the height.

Thus, the total perimeter of the frame is given by

Area of the four side faces of the aquarium is 4 times the length of the base times the height =

Total area to be covered by grass is the base and the four side faces and is given by

Cost of the entire metal frame =

Cost of the entire grass =

Therefore, total cost in terms of the height, h, is given by