An open-topped glass aquarium with a square base is designed to hold 4 cubic feet of water. What is the minimum exterior surface area of the aquarium? square feet

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Define Volume Formula: Let s be the side length of the square base of the aquarium. The volume of the aquarium is the cube of the side length since it's a square base. V = s^3Substitute Volume Value: Volume of aquarium: 4 cubic feet Substitute 4 for V in V = s^3. 4 = s^3Find Side Length: Find the side length s. 4 = s^3 s = cube root of 4 s ≈ 1.5874 feet (rounded to 4 decimal places)Calculate Surface Area Formula: Calculate the exterior surface area of the aquarium. The surface area of a square-based open-topped box is the area of the base plus the area of the four sides. Surface Area = s^2 + 4(s * h) But since the height h is the same as the side length s (because the volume is a cube of the side length), we can simplify this to: Surface Area = s^2 + 4(s * s) Surface Area = s^2 + 4s^2 Surface Area = 5s^2Substitute Side Length: Substitute the side length s into the surface area formula. Surface Area = 5 * (1.5874)^2 Surface Area ≈ 5 * 2.5197 Surface Area ≈ 12.5985 square feet

An open-topped glass aquarium with a square base is designed to hold $4$ cubic feet of water. What is the minimum exterior surface area of the aquarium? $\newline$ square feet

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An open-topped glass aquarium with a square base is designed to hold $4$ cubic feet of water. What is the minimum exterior surface area of the aquarium? $\newline$ square feet