Shape and Space: Measurement (Circles, Area, Volume) and 3-D Objects
Measurement questions ask you to choose the right formula, substitute carefully, and report units correctly.
For circles, know both relationships: circumference C = πd = 2πr and area A = πr². The diameter is twice the radius, so a circle with diameter 10 cm has r = 5 cm, area 25π ≈ 78.5 cm², and circumference 10π ≈ 31.4 cm.
Area formulas: rectangle A = lw; parallelogram A = bh using the perpendicular height, not a slant side; triangle A = bh ÷ 2; trapezoid A = (a + b)h ÷ 2. Composite figures are split into these shapes, areas added, and any overlapping region subtracted.
Volume of a right prism or cylinder is base area times height: V = lwh or V = πr²h. Surface area is the total area of all faces - unfold the object into a net and find each face rather than guessing a formula.
Traps: substituting the diameter into A = πr²; mixing units, such as multiplying 20 cm by 0.3 m without converting; writing cm instead of cm² or cm³; and converting area units by 100 instead of 10 000 (1 m² = 10 000 cm²).
Worked example: a cylinder has radius 3 cm and height 10 cm. V = πr²h ≈ 3.14 × 9 × 10 = 282.6 cm³. Rule of thumb: name the shape, write the formula, substitute with units attached, then check that the unit of the answer matches what was asked - length, area, or volume.