Percentage increase in surface area after cutting a 4 cm cube into 1 cm cubes:

To solve this problem, we need to calculate the surface area before and after cutting the cube into smaller cubes and then find the percentage increase.

Step 1: Calculate the surface area before cutting:
The surface area of a cube can be calculated using the formula: 6a^2, where a is the length of one side of the cube.

Given that the length of one side of the cube is 4 cm, we can calculate the surface area before cutting as follows:
Surface Area before cutting = 6 * (4 cm)^2
= 6 * 16 cm^2
= 96 cm^2

Step 2: Calculate the surface area after cutting:
When a cube is cut into smaller cubes, the surface area of each smaller cube is added up to find the total surface area.

Since the cube is cut into 1 cm cubes, the number of smaller cubes will be equal to the volume of the larger cube.
Volume of the larger cube = (4 cm)^3
= 64 cm^3

Therefore, there will be 64 smaller cubes after cutting.

The surface area of each smaller cube is 6 * (1 cm)^2 = 6 cm^2.

The total surface area after cutting will be the surface area of each smaller cube multiplied by the number of smaller cubes:
Surface Area after cutting = 6 cm^2 * 64
= 384 cm^2

Step 3: Calculate the percentage increase in surface area:
To find the percentage increase, we need to calculate the difference between the surface area after cutting and the surface area before cutting, and then express it as a percentage of the surface area before cutting.

Difference = Surface Area after cutting - Surface Area before cutting
= 384 cm^2 - 96 cm^2
= 288 cm^2

Percentage Increase = (Difference / Surface Area before cutting) * 100
= (288 cm^2 / 96 cm^2) * 100
= 300%

Therefore, the percentage increase in the surface area after cutting the 4 cm cube into 1 cm cubes is 300%.

Hence, the correct answer is option B) 300%.