To solve this problem, let`s first calculate the volume of each small ball. The formula for the volume of a sphere is (4/3) * π * r^3, where r is the radius.

Since the radius of each small ball is 1 cm, we can substitute the value into the formula and calculate the volume of each ball:

Volume = (4/3) * π * (1^3)

= 4/3 * π

Now, let`s find the total volume of all eight small balls by multiplying the volume of each small ball by 8:

Total Volume = 8 * (4/3) * π

Next, we need to find the radius of the new ball that is formed by melting all the small balls. We know that the volume of a sphere is given by (4/3) * π * r_new^3, where r_new is the radius of the new ball.

Since the total volume of the small balls is equal to the volume of the new ball, we can equate the two volumes:

8 * (4/3) * π = (4/3) * π * r_new^3

Simplifying the equation:

8 = r_new^3

To find the