Your school is planning to put an aquarium with 30 fish in it in the main lobby. To accommodate this number of fish, the aquarium should be between 50 and 60 cubic feet of water. To help reduce costs, the surface area of the aquarium should be no more than 80 feet square. Do not include the area of the top in your calculation of surface area.
To find the dimensions of the aquarium, we need to consider a few factors: the volume of water required, the range of acceptable volumes, and the surface area limitation.
1. Volume of water:
The volume of water needed to accommodate 30 fish depends on the type and size of the fish. Assuming average-sized fish, a general guideline is to allow about one gallon of water per one inch of fish length. Let's calculate the minimum and maximum volume required.
Minimum volume: Assuming each fish is about 2 inches long on average, we need 30 * 2 = 60 inches of fish length. Since 1 gallon is approximately 231 cubic inches, the minimum volume required would be 60 / 231 = 0.26 gallons. Converted to cubic feet, this is approximately 0.0036 cubic feet (1 gallon ≈ 0.1337 cubic feet).
Maximum volume: Assuming each fish is about 6 inches long on average (considering larger fish), we would need 30 * 6 = 180 inches of fish length. This corresponds to a volume of 180 / 231 ≈ 0.78 gallons or approximately 0.104 cubic feet.
Thus, the aquarium should have a volume between 0.0036 and 0.104 cubic feet.
2. Surface area limitation:
The surface area of the aquarium should not exceed 80 square feet, excluding the top.
Since the aquarium is likely to have a rectangular shape, we need to find the dimensions that satisfy the volume requirements while not exceeding the surface area limitation.
Let's assume the length of the aquarium is L, the width is W, and the height (which affects volume) is H.
Volume equation: L * W * H = Volume (between 0.0036 and 0.104 cubic feet).
Surface area equation: 2*(L * W) + 2*(H * W) = Surface Area (excluding the top, ≤ 80 square feet).
We need to solve these equations simultaneously to find suitable dimensions for the aquarium within the given restrictions.
Since this requires a numerical solution, we will use a computer program or a spreadsheet to find the appropriate values of L, W, and H.