The formula to calculate the volume $V$ of a cube is:

$V = \text{edge}^3$

Given that the edge of the cube is 2.01 cm, we calculate the volume as follows:

$V = (2.01)^3 = 2.01 \times 2.01 \times 2.01 = 8.120601 \, \text{cm}^3$

Now, comparing this result to the options:

1. 8.120601 cm³ — This is the exact result.
2. 8.120 cm³ — Rounded to three decimal places.
3. 8.1 cm³ — Rounded to one decimal place.
4. 8.12 cm³ — Rounded to two decimal places.

Since the closest reasonable rounding is to two decimal places, the best answer is:

4. 8.12 cm³

Would you like a detailed breakdown of how the rounding was done?

Here are five related questions:

1. What is the formula for the surface area of a cube?
2. How would the volume change if the edge of the cube were doubled?
3. How do you calculate the volume of other 3D shapes like spheres or cylinders?
4. What is the volume of a cube with an edge length of 3.5 cm?
5. How can you calculate the cube root of a number manually?

Tip: When rounding, consider the number of decimal places needed based on the precision of the given data.