The value of a number cube is 3⁶ cubic millimeters. Find the length of one side of de number cube.

To find the length of one side of the cube, we use the formula for the volume of a cube:

\[
V = s^3
\]

where \(V\) is the volume and \(s\) is the side length. You are given that the volume of the cube is \(3^6\) cubic millimeters, so:

\[
s^3 = 3^6
\]

Now, take the cube root of both sides to solve for \(s\):

\[
s = \sqrt[3]{3^6}
\]

We can simplify this:

\[
s = 3^{6/3} = 3^2 = 9
\]

Thus, the length of one side of the cube is 9 millimeters.

Would you like further clarification or details? Here are some related questions:

1. What is the volume of a cube if one side length is 5 millimeters?
2. How would you calculate the surface area of the cube with side length 9 mm?
3. If the side length of a cube is doubled, how does the volume change?
4. Can you find the side length of a cube whose volume is 64 cubic millimeters?
5. What is the difference between surface area and volume for a cube?

**Tip:** Remember that the volume of a cube grows much faster than its surface area as the side length increases.

The value of a number cube is 3⁶ cubic millimeters. Find the length of one side of the number cube.

Learn how to calculate the side length of a cube with a volume of 3^6 cubic millimeters. This problem involves geometric concepts and properties of exponents, offering a step-by-step solution. Suitable for middle school students in Grades 6-8.

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