If each edge of a cube is increased by 50%, the percentage increase in the surface area is :

Let the original edge be a. Surface area of a cube is 6a². When each edge increases by 50%, the new edge is 1.5a, so the new surface area is 6(1.5a)² = 6 × 2.25a² = 13.5a². The increase is 7.5a² on an original 6a², which is 1.25, or 125%. Option D is correct.

The core concept is that area scales with the square of a linear change. A factor of 1.5 in length gives a factor of 1.5² = 2.25 in area, so the percentage increase is 125%.

• A (50%) is the linear increase in edge length. Area does not grow at the same rate as length.
• B (75%) has no valid derivation under the square law. It would need an area factor of 1.75, which 1.5 does not produce.
• C (100%) would need the area to double, which requires an edge factor of √2, not 1.5.

This scaling idea recurs in mensuration and in Mains questions on how material requirements and costs scale with size. Volume, by contrast, scales with the cube of the factor, giving 237.5%.

Trap: assuming surface area grows at the same percentage as the edge and marking A.