To determine who is correct between Diane and Gina, we need to find the length of a side of the cube given the volume of the cube, which is 475 cubic inches.

The formula for the volume of a cube is:

$V = s^3$

where $V$ is the volume and $s$ is the side length of the cube.

We can find the approximate side length by taking the cube root of the volume:

$s = \sqrt[3]{V}$

Substitute $V = 475$:

$s = \sqrt[3]{475}$

Now, let's calculate the cube root of 475 to determine the side length.

The cube root of 475 is approximately $7.80$ inches.

Since 7.80 inches is closer to 8 inches than to 7 inches, Gina is correct in thinking the length of the side of the cube is closer to 8 inches.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you calculate the surface area of a cube with side length 7.80 inches?
2. What is the exact cube root of 475, and how does it differ from an approximate value?
3. How would the volume change if the side length were exactly 7 or 8 inches?
4. What is the relationship between surface area and volume for a cube?
5. How can you use the cube formula to solve real-life problems involving storage?

Tip: For quick estimates of cube roots, memorize cube numbers of small integers (e.g., $2^3 = 8$, $3^3 = 27$, etc.) for comparison.