Math Problem Statement

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

Solution

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

V=s3V = s^3

where VV is the volume and ss is the side length. You are given that the volume of the cube is 363^6 cubic millimeters, so:

s3=36s^3 = 3^6

Now, take the cube root of both sides to solve for ss:

s=363s = \sqrt[3]{3^6}

We can simplify this:

s=36/3=32=9s = 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.

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Math Problem Analysis

Mathematical Concepts

Geometry
Exponentiation
Cube Root

Formulas

Volume of a cube: V = s^3
Cube root: s = V^(1/3)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 6-8