Mensuration
What you must know
Know the area formulas for rectangles, triangles (half base times height), parallelograms, trapeziums (half the sum of parallel sides times height) and circles (pi r^2), and the circumference formula C = 2 pi r. For sectors, arc length = (theta/360) x 2 pi r and sector area = (theta/360) x pi r^2. Solids: volume of a prism = area of cross-section x length; cylinder V = pi r^2 h; cone V = one third pi r^2 h; sphere V = four thirds pi r^3; pyramid V = one third x base area x height. Surface areas include curved faces: cylinder 2 pi r h, cone pi r l (l the slant height), sphere 4 pi r^2. Convert units carefully (1 m = 100 cm, so 1 m^2 = 10 000 cm^2 and 1 m^3 = 1 000 000 cm^3). Similar figures: lengths scale by k, areas by k^2, volumes by k^3.
Traps
- Diameter given but radius needed: halve it first.
- Slant height is not the perpendicular height; use Pythagoras to find it.
- Total surface area includes the circular ends; curved surface area does not.
- Mixing cm and m in one calculation.
- Composite solids: add or subtract the correct parts and avoid counting hidden faces twice.
Rule of thumb
Write the formula, substitute with units visible, then check the answer is sensible (a volume in cm^3, an area in cm^2).
Example: a cylinder of radius 7 cm and height 10 cm has V = pi x 7^2 x 10, which is about 1 540 cm^3 using pi = 22/7.