Question

A cuboid of dimension \(12 cm \times 16 cm \times 20 cm\) is cut into small cubes of edge length 4 cm. What is the difference between the total surface area of the original cuboid and the sum of the surface area of all the small cubes?

• A. 5008 cm²
• B. 4256 cm²
• C. 1408 cm²
• D. 0 cm²

Answer 1

The Correct Option is B

Surface Area Calculation 

- The given dimensions of the cuboid are 12 cm, 16 cm, and 20 cm.

- The total surface area of the original cuboid is calculated using the formula:

\[ A_{\text{cuboid}} = 2(lw + lh + wh) \]

Substituting the values:

\[ A_{\text{cuboid}} = 2(12 \times 16 + 12 \times 20 + 16 \times 20) \] \[ = 2(192 + 240 + 320) = 2 \times 752 = 1504 \text{ cm²} \]

- Next, we calculate the total surface area of all the small cubes. The cuboid is divided into small cubes of edge length 4 cm.

- The number of cubes is:

\[ \text{Number of cubes} = \frac{12 \times 16 \times 20}{4 \times 4 \times 4} = 3840 \]

- The surface area of each small cube is:

\[ A_{\text{small cube}} = 6 \times 4^2 = 6 \times 16 = 96 \text{ cm²} \]

- The total surface area of all the small cubes is:

\[ A_{\text{total small cubes}} = 60 \times 96 = 5760 \text{ cm²} \]

- The difference between the total surface area of the small cubes and the original cuboid is:

\[ \text{Difference} = 5760 - 1504 = 4256 \text{ cm²} \]

Conclusion: The difference in surface areas is 4256 cm².