Final answer:
The expression that represents the side length of Cynthia's cubic jewelry box with volume v cubic inches is s = 3√v. This is derived by taking the cube root of the volume, following the formula for volume of a cube, V = s3.
Step-by-step explanation:
Cynthia has a jewelry box that is shaped like a cube, with a volume of v cubic inches. To find the side length of this cube, we must consider the formula for the volume of a cube, which is V = s3, where V is the volume and s is the side length of the cube. To represent the side length in terms of the volume, we need to take the cube root of the volume. Therefore, the expression that represents the side length of the jewelry box in inches would be s =3√v.
The cube root operation undoes the cubing operation, so by taking the cube root of the volume, we can find the original side length that, when cubed, gives us the volume v. Cubes are perfect for explaining this concept because all sides are equal, and hence, the volume is the product of three identical factors. This example is echoed in various scenarios, from small jewelry boxes to understanding the geometry of Rubik's cubes and comparing the surface area to volume ratios in geometry and biology.