Full solution

Q. An open-topped glass aquarium with a square base is designed to hold

13

5

cubic feet of water. What is the minimum exterior surface area of the aquarium?

\newline

square feet

Define Side Length: Let $s$ be the side length of the square base of the aquarium. $\newline$ Volume of the aquarium is the cube of the side length since it's a square base. $\newline$ $V = s^3$
Volume Calculation: Volume of the aquarium: $13.5$ cubic feet. $\newline$ Substitute $13.5$ for $V$ in $V = s^3$ . $\newline$ $13.5 = s^3$
Find Side Length: Find the side length $s$ . $\newline$ Take the cube root of both sides. $\newline$ $s = \sqrt[3]{13.5}$ $\newline$ $s \approx 2.381$
Calculate Surface Area: Calculate the exterior surface area of the aquarium. $\newline$ Surface area of a cube without the top is $S = 4s^2 + s^2$ (four sides and the base). $\newline$ Substitute $s \approx 2.381$ into $S = 4s^2 + s^2$ . $\newline$ $S = 4(2.381)^2 + (2.381)^2$
Calculate Surface Area: Calculate the exterior surface area of the aquarium. $\newline$ Surface area of a cube without the top is $S = 4s^2 + s^2$ (four sides and the base). $\newline$ Substitute $s \approx 2.381$ into $S = 4s^2 + s^2$ . $\newline$ $S = 4(2.381)^2 + (2.381)^2$ Perform the calculation. $\newline$ $S = 4(5.665) + 5.665$ $\newline$ $S = 22.660 + 5.665$ $\newline$ $S \approx 28.325$