Questions: 4. ALGAE Ronald owns a fish tank in the shape of a rectangular box. The tank is 18 inches high, 14 inches deep, and 30 inches long. Ronald went on a one-month vacation. When he returned he found that the sides and bottom of his fish tank were covered with algae. What is the area that was covered?

Solution Steps

To find the area covered by algae, we need to calculate the surface area of the inside of the fish tank. This includes the area of the bottom and the four sides. The top is not included since it is open. The surface area can be calculated by finding the area of each side and summing them up.

The bottom of the tank is a rectangle with dimensions 30 inches (length) and 14 inches (depth). The area of the bottom is calculated as: \[ \text{Bottom Area} = \text{length} \times \text{depth} = 30 \times 14 = 420 \, \text{square inches} \]

Each of the two long sides of the tank is a rectangle with dimensions 30 inches (length) and 18 inches (height). The combined area of these two sides is: \[ \text{Side Area 1} = 2 \times (\text{length} \times \text{height}) = 2 \times (30 \times 18) = 1080 \, \text{square inches} \]

Each of the two short sides of the tank is a rectangle with dimensions 14 inches (depth) and 18 inches (height). The combined area of these two sides is: \[ \text{Side Area 2} = 2 \times (\text{depth} \times \text{height}) = 2 \times (14 \times 18) = 504 \, \text{square inches} \]

The total area covered by algae is the sum of the areas of the bottom and the four sides: \[ \text{Total Area} = \text{Bottom Area} + \text{Side Area 1} + \text{Side Area 2} = 420 + 1080 + 504 = 2004 \, \text{square inches} \]

Final Answer