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An open-topped glass aquarium with a square base is designed to hold 62.5 cubic feet of water. What is the minimum possible exterior surface area of the aquarium? square feet

An open-topped glass aquarium with a square base is designed to hold 6262.55 cubic feet of water. What is the minimum possible exterior surface area of the aquarium?\newlinesquare feet

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Q. An open-topped glass aquarium with a square base is designed to hold 6262.55 cubic feet of water. What is the minimum possible exterior surface area of the aquarium?\newlinesquare feet
  1. Find Height of Aquarium: First, let's find the height of the aquarium assuming it's a perfect cube, which would give us the minimum surface area. The volume of a cube is given by V=s3V = s^3, where ss is the side length. So, we need to find the cube root of 62.562.5 cubic feet.
  2. Calculate Cube Root: Calculate the cube root of 62.562.5 to find the side length.\newlines=62.53s = \sqrt[3]{62.5}\newlines≈3.97s \approx 3.97 feet (rounded to two decimal places)
  3. Calculate Surface Area: Now, we calculate the surface area of the cube, but since the aquarium is open-topped, we only need to calculate the area of the four sides and the base. The surface area of a cube is 6s26s^2, but we need to subtract one side for the open top.\newlineSurface area = 5s25s^2
  4. Plug in Side Length: Plug in the side length to find the surface area.\newlineSurface area =5×(3.97)2= 5 \times (3.97)^2\newlineSurface area ≈5×15.76\approx 5 \times 15.76\newlineSurface area ≈78.8\approx 78.8 square feet

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