Find surface area and interpret nets of 3D solids.
Free, timed SHSAT practice sets on surface area & nets— every question includes a full worked explanation, and there's no account required.
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Surface area is the total area of every face of a solid, as if you unfold it flat into a net and add up all the pieces.
Common traps: adding the three face areas and forgetting to double them, counting only one circle on a cylinder, leaving out the top and bottom of a cube, and cubing the side (that is volume, not surface area).
There are 3 pairs of matching faces, so surface area \(= 2(lw + lh + wh) = 2(180 + 72 + 40) = 584\) sq m. (Multiplying \(18 \times 10 \times 4\) gives the volume, 720. Counting each face only once, \(180 + 72 + 40\), gives 292. Counting only the 4 side faces and leaving out the top and bottom gives 224.)
Surface area \(= 2\pi r h + 2\pi r^2 = 2\pi(11)(20) + 2\pi(11)^2 = 682\pi\) sq m. (Counting only one circular end gives \(561\pi\). Counting only the curved side and no circles gives \(440\pi\). Using the volume formula \(\pi r^2 h\) gives \(2420\pi\).)
A net made of one circle and one sector (a 'pie-slice' shape) folds up into a cone. (A cylinder would need two circles and one rectangle. A square pyramid would need one square and four triangles. A sphere has no flat net at all.)