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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 $62$ . $5$ cubic feet of water. What is the minimum possible exterior surface area of the aquarium? $\newline$ square feet

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Area and perimeter: word problems

Full solution

Q. 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?

\newline

square feet

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 $V = s^3$ , where $s$ is the side length. So, we need to find the cube root of $62.5$ cubic feet.
Calculate Cube Root: Calculate the cube root of $62.5$ to find the side length. $\newline$ $s = \sqrt[3]{62.5}$ $\newline$ $s \approx 3.97$ feet (rounded to two decimal places)
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 $6s^2$ , but we need to subtract one side for the open top. $\newline$ Surface area = $5s^2$
Plug in Side Length: Plug in the side length to find the surface area. $\newline$ Surface area $= 5 \times (3.97)^2$ $\newline$ Surface area $\approx 5 \times 15.76$ $\newline$ Surface area $\approx 78.8$ square feet

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