Diane and Gina have cube shaped bins to store their items on shelves. The volume of each storage cube is 475 cubic inches. The length of each side of the cube must be between 7 and 8 inches. Diane thinks the length of the side of the cube is closer to 7 inches and Gina thinks the length of the side of the cube is closer to 8 inches. Who is correct?

 

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.

Diane and Gina have cube shaped bins to store their items on shelves. The volume of each storage cube is 475 cubic inches. The length of each side of the cube must be between 7 and 8 inches. Diane thinks the length of the side of the cube is closer to 7 inches and Gina thinks the length of the side of the cube is closer to 8 inches. Who is correct?

Learn how to calculate the side length of a cube with a volume of 475 cubic inches by using the cube root formula. This geometry problem helps to understand cubic measurements and approximations. Suitable for students in Grades 6-8.

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