If each edge of the cube increases by 1 cm, then its volume increases 125 times, find the edge?

Let x be the size of the edge before increasing. Then x + 1 will be after the increase. Let’s write a system of equations for the volume of a cube:

x ^ 3 = V, where V is the volume of the cube.

(x + 1) ^ 3 = 125V.

Let’s solve this system of equations.

(x + 1) ^ 3 = 125×3;

Let’s solve this equation. Let’s extract the cube root from the right and left sides:

x + 1 = 5x;

5x – x = 1;

4x = 1;

x = 1: 4 = 0.25 cm.

Answer: The length of the edge of the cube is 0.25 cm.