Measurement and Geometric Modeling
This domain covers perimeter, area, surface area, volume, and modeling real objects. Know the area formulas: rectangle (base times height), triangle (one half base times height), parallelogram (base times height), trapezoid (one half times the sum of the bases times height), and circle (pi r squared). For solids: prism and cylinder volume = base area times height; pyramid and cone volume = one third times base area times height; sphere volume = four thirds pi r cubed. Surface area is the sum of all face areas; for a cylinder it is 2 pi r squared plus 2 pi r h, and for a sphere it is 4 pi r squared.
Modeling questions often involve composite figures: add areas of parts, or subtract a cutout (like a circle removed from a square). Density and population problems use volume or area as the multiplier. Also expect the effect of scaling: if every linear dimension is multiplied by k, area scales by k squared and volume scales by k cubed, so doubling a radius multiplies volume by 8.
Traps: using slant height instead of perpendicular height in cone and pyramid volume; forgetting units (square vs cubic); leaving answers in terms of pi when a decimal is requested; and mixing up surface area with volume. Read whether the question asks for capacity (volume) or material needed (surface area).
Worked example. A cylinder has radius 3 and height 10. Volume = pi times 9 times 10 = 90 pi, about 282.7 cubic units. Surface area = 2 pi (9) + 2 pi (3)(10) = 18 pi + 60 pi = 78 pi, about 245.0 square units.