Surface area change after melting to a cube: A solid block (27 cm × 8 cm × 1 cm) is melted and recast into a cube. Find the difference between the surface areas of the original block and the new cube (in cm2).

Introduction / Context:Melting conserves volume. We first find the cube’s side from equal volume, then compute both surface areas and take the difference. This tests volume conservation and area formulas.

Given Data / Assumptions:

• Rectangular solid: 27 × 8 × 1 cm
• Volume is conserved.

Concept / Approach:

• V_block = l*b*h.
• Let cube side = a with a^3 = V_block.
• Compute SA_block and SA_cube and subtract.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 296/300/284 cm2: Small arithmetic deviations, not matching exact computations.

Common Pitfalls:

• Using perimeter-like ideas instead of surface area.
• Forgetting both small faces 8*1 and 27*1 contribute to SA.

Final Answer:

286 cm2