The surface area of the cardboard box above is 3,456 square inches. If the box is a cube, what are the dimensions of the box? Part A: What formula can be used to solve this problem? Part B: What are the dimensions of the box? Part C: Show the steps for Part B.

To find the dimensions of a cube from its surface area, you can use the formula for the surface area of a cube: \( A = 6s^2 \), where \( s \) is the length of one side of the cube. Since the total surface area is 3,456 square inches in this scenario, you can set up the equation: \( 6s^2 = 3,456 \). To find the dimensions of the cube, you will first divide the surface area by 6. That gives you \( s^2 = \frac{3,456}{6} = 576 \). Next, take the square root of 576 to find \( s \). Therefore, \( s = 24 \) inches. Consequently, the dimensions of the box are 24 inches on each side. A fun fact about cubes is that they are one of the simplest three-dimensional shapes. The regularity of a cube lends itself to various benefits in design and architecture, offering optimal space usage and stability. When a cube is used in practical settings, such as packaging, it maximizes storage and minimizes waste. It’s essential to remember that when working with surface area, one common mistake is forgetting that a cube has six faces. Always double-check your multiplication and division to ensure you're dividing by 6 and not another number. Also, ensure correct application of the square root; it can be easy to miscalculate if you're not careful with your arithmetic!