Volume and surface area
Circles
Circumference = 2πr = πd. Area = πr².
Edexcel Paper 1 may ask for exact answers in terms of π (e.g. "leave your answer in terms of π").
Cylinders
Volume = πr²h. Curved surface area = 2πrh. Total surface area = 2πrh + 2πr².
Cones
Volume = ⅓πr²h. Curved surface area = πrl, where l = slant height = √(r² + h²). Total surface area = πrl + πr².
Spheres
Volume = (4/3)πr³. Surface area = 4πr².
Pyramids
Volume = ⅓ × base area × perpendicular height. (This applies to any pyramid, including a square-based pyramid.)
Composite shapes
Edexcel frequently combines solids: a hemisphere on a cylinder, a cone on a sphere, etc. Break into components, calculate each part, and add (or subtract for hollows).
Exact answers in terms of π
On Paper 1, "leave in terms of π" means do NOT evaluate numerically. Write the answer as, e.g., 48π cm³.
Units
Volume: cm³, m³, mm³ (cubic). Surface area: cm², m² (square). Always state the unit in your final answer.
⚠Common mistakes
- Using diameter instead of radius: many students substitute d into formulas requiring r.
- Forgetting ⅓ in cone/pyramid volume.
- Slant height ≠ perpendicular height in cone: always calculate l = √(r² + h²) from the perpendicular height.
- Not adding both circular ends when finding total surface area of a cylinder.
- Wrong units: volume is cubic, area is square.
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