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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
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