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Question

# Your friend is comparing two 6-sided cubic storage bins. The yellow bin has a surface area of 9600 square centimeters and costs $25. The blue bin has a surface area of 7350 square centimeters and costs$20. a. Find the edge length of each bin. b. Which bin costs less per cubic centimeter? Explain your reasoning.

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(a) $\textbf{Edge lengths}$

You have the next information: % for bullets

• The surface area of the $\text{\color{#965501}yellow}$ bin is $9600\text{ cm}^2$
• The surface area of the $\text{\color{#4257b2}blue}$ bin is $7350\text{ cm}^2$

Since each bin is $6$-sided cubic, it menas their surface area consists of $6$ squares.

The surfrace of each square of $\text{\color{#965501}yellow}$ bin is $9600\text{ cm}^2\div 6=\color{#965501}1600\text{ cm}^2$

The surfrace of each square of $\text{\color{#4257b2}blue}$ bin is $7350\text{ cm}^2\div 6=\color{#4257b2}1225\text{ cm}^2$

Since area of a square is given by $A=l^2$ where $l$ is its side length, then the length is given by

$\color{#c34632}l=+\sqrt{A}$

Let $\color{#965501}l_Y$ be the side length of the yellow bin and $\color{#4257b2}l_B$ the side length of the blue bin.

Now we have:

\begin{align*} {\color{#965501}l_Y}&=+\sqrt{1600\text{ cm}^2}=\boxed{\color{#965501} 40\text{ cm}} \\ {\color{#4257b2}l_B}&=+\sqrt{1225\text{ cm}^2}=\boxed{\color{#4257b2} 35\text{ cm}} \end{align*}

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