Question

A 4 cm cube is cut into 1cm cubes. What is the percentage increase in the surface area after such cutting?

• A. 4%
• B. 300%
• C. 75%
• D. 400%

Answer 1

The Correct Option is B

To solve the problem of finding the percentage increase in the surface area after cutting a 4 cm cube into 1 cm cubes, follow these steps:

Step 1: Calculate the surface area of the original cube. 

A cube with side length 4 cm has a surface area calculated by the formula:

\( \text{Surface Area} = 6 \times (\text{side length})^2 \).

For a 4 cm cube:

\( \text{Surface Area} = 6 \times (4)^2 = 6 \times 16 = 96 \, \text{cm}^2 \).

Step 2: Determine the total surface area of the smaller 1 cm cubes.

The volume of the original 4 cm cube is \( 4^3 = 64 \, \text{cm}^3 \).

Cut into 1 cm cubes, we have 64 smaller cubes since each 1 cm cube has a volume of \( 1^3 = 1 \, \text{cm}^3 \).

Each smaller cube has a surface area of \( 6 \times (1)^2 = 6 \, \text{cm}^2 \).

Therefore, the total surface area of the 64 smaller cubes is:

\( 64 \times 6 = 384 \, \text{cm}^2 \).

Step 3: Calculate the percentage increase in surface area.

The increase in surface area is \( 384 - 96 = 288 \, \text{cm}^2 \).

The percentage increase is:

\( \left(\frac{288}{96}\right) \times 100\% = 300\% \).

Therefore, the percentage increase in surface area after cutting is 300%.