Math Problem Statement

If you have a cube with a volume of 73.560059, what is the length of the cube? Please show your work

Solution

To find the length of a cube when the volume is given, we use the formula for the volume of a cube:

V=s3V = s^3

where VV is the volume and ss is the length of a side (edge) of the cube.

Given that the volume VV is 73.560059, we need to solve for ss by taking the cube root of the volume:

s=73.5600593s = \sqrt[3]{73.560059}

Calculating the cube root:

s73.56005934.222s \approx \sqrt[3]{73.560059} \approx 4.222

Thus, the length of each side of the cube is approximately 4.222 units.

Would you like more details or have any questions about this calculation?

Here are five related questions for further exploration:

  1. How would the volume change if the length of the cube's side doubled?
  2. What would be the surface area of a cube with a side length of 4.222?
  3. How do you calculate the diagonal of a cube given the side length?
  4. What is the formula for the surface area of a cube, and how is it derived?
  5. How does the volume of a cube compare to that of other geometric shapes with the same side length?

Tip: Remember, to find the edge length of any cube given its volume, you always take the cube root of the volume.

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Math Problem Analysis

Mathematical Concepts

Geometry
Cube Volume
Cube Root

Formulas

Volume of a Cube: V = s^3
Cube Root: s = ∛V

Theorems

Properties of Cubes

Suitable Grade Level

Grades 6-8