Given:
- Edge of the original cube = 10 cm

To find:
- Ratio of the edge of the smaller cube to the edge of the bigger cube

Explanation:

To solve this problem, we need to understand the concept of volume and how it relates to the dimensions of a cube.

Volume of a Cube:
The volume of a cube is calculated by multiplying the length of one edge by itself twice. In formula form, it can be written as:
Volume = edge³

Original Cube:
The edge of the original cube is given as 10 cm. Therefore, the volume of the original cube can be calculated as:
Volume of original cube = 10³ = 1000 cm³

Two Equal Cubes:
When the original cube is melted, it forms two equal cubes. Let's assume the edge of each smaller cube is x cm.

Volume of Smaller Cube:
The volume of each smaller cube can be calculated as:
Volume of smaller cube = x³

Since the smaller cubes are equal in size, the total volume of the two smaller cubes combined is equal to the volume of the original cube.

So, the total volume of the two smaller cubes can be written as:
Total volume of smaller cubes = 2 * Volume of smaller cube
Total volume of smaller cubes = 2 * x³

Since the total volume of the smaller cubes is equal to the volume of the original cube, we can equate the two expressions:

2 * x³ = 1000

Solving for x:
To find the value of x, we can divide both sides of the equation by 2:
x³ = 1000 / 2
x³ = 500

Taking the cube root of both sides, we find:
x = ∛500

Calculating the Ratio:
Now that we know the value of x, we can calculate the ratio of the edge of the smaller cube to the edge of the bigger cube:
Ratio = x / 10

Substituting the value of x, we get:
Ratio = ∛500 / 10

Simplifying further, we find:
Ratio ≈ 1.71

Therefore, the ratio of the edge of the smaller cube to the edge of the bigger cube is approximately 1.71.