Question

Three cubes of metal with edges 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube. What is the lateral surface area of the new formed cube?

• A. 72 cm\(^2\)
• B. 144 cm\(^2\)
• C. 128 cm\(^2\)
• D. 256 cm\(^2\)

Hint:

The lateral surface area of a cube is calculated by \( 4 \times \text{side}^2 \).

Answer 1

The Correct Option is B

The total volume of the three cubes is the sum of their individual volumes: \[ \text{Volume of 1st cube} = 3^3 = 27 \, \text{cm}^3, \quad
\text{Volume of 2nd cube} = 4^3 = 64 \, \text{cm}^3, \quad
\text{Volume of 3rd cube} = 5^3 = 125 \, \text{cm}^3. \] \[ \text{Total volume} = 27 + 64 + 125 = 216 \, \text{cm}^3. \] Now, the side length of the new cube is: \[ \text{Side of new cube} = \sqrt[3]{216} = 6 \, \text{cm}. \] The lateral surface area of the new cube is: \[ \text{Lateral Surface Area} = 4 \times \text{side}^2 = 4 \times 6^2 = 4 \times 36 = 144 \, \text{cm}^2. \] Thus, the correct answer is 144 cm\(^2\).