Surface area is the total area of all the outer faces, measured in square units — think of it as the amount of wrapping paper or paint needed to cover the solid. A box has three pairs of matching faces, so its surface area is 2(lw + lh + wh). A cube’s six identical square faces give the tidy 6s². A cylinder’s surface is the two circular ends (2πr²) plus the unrolled curved side (2πrh), which factor together as 2πr(r + h). The common GRE trap is confusing surface area with volume — one is square units of covering, the other is cubic units of filling — so read whether the question asks about covering the outside or filling the inside. Reverse questions on a cube divide the surface area by 6 and take a square root to find the edge.
✅ Solved examples
1. A box measures 3 by 4 by 5. Find its surface area.
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