Topic 7 of 11 · Form 2
Mensuration
Rectangle, triangle (½bh or ½ab sin C), parallelogram, trapezium (½(a + b)h), circle (A = πr², C = 2πr), compound shapes.
Notes for this topic 1 file, in order
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Perimeter and area
Rectangle, triangle (½bh or ½ab sin C), parallelogram, trapezium (½(a + b)h), circle (A = πr², C = 2πr), compound shapes.
Arcs and sectors
Arc length = (θ/360) × 2πr; sector area = (θ/360) × πr².
Worked example: Find the area of a sector of radius 9 cm and angle 80°.
(80/360) × π × 81 = 56.5 cm²
Surface area and volume
- Prism: V = area of cross-section × length.
- Cylinder: V = πr²h; curved surface area = 2πrh.
- Cone: V = ⅓πr²h; curved surface = πrl.
- Sphere: V = (4/3)πr³; surface area = 4πr².
- Pyramid: V = ⅓ × base area × height.
Worked example: Find the volume of a cone with radius 6 cm and height 10 cm.
⅓ × π × 36 × 10 = 377 cm³
Units
1 m² = 10 000 cm²; 1 m³ = 1 000 000 cm³; 1 litre = 1 000 cm³.
Exam tip: Check whether a question asks for curved surface area or total surface area.
Check yourself
- Find the circumference of a circle of diameter 14 cm.
- A cylinder has radius 3 cm and height 8 cm. Find its volume.
- Convert 2.5 m² to cm².
Show answers
- 44.0 cm (14π)
- 72π ≈ 226 cm³
- 25 000 cm²
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