ZIMSEC O Level · Mathematics · Form 1, Form 2, Form 3, Form 4
Mensuration is the measurement of lengths, areas and volumes.
Units
1 km = 1000 m; 1 m = 100 cm; 1 m² = 10 000 cm²; 1 m³ = 1 000 000 cm³; 1 litre = 1000 cm³; 1 hectare = 10 000 m².
Areas
- Rectangle: length × width. Triangle: ½ × base × height.
- Parallelogram: base × height. Trapezium: ½(a + b)h.
- Circle: area = πr²; circumference = 2πr.
- Sector with angle θ: area = (θ/360) × πr²; arc length = (θ/360) × 2πr.
Volumes and surface areas
- Prism or cylinder: volume = area of cross-section × length. Cylinder: V = πr²h.
- Cone: V = ⅓πr²h. Pyramid: V = ⅓ × base area × height. Sphere: V = (4/3)πr³.
- Curved surface area of a cylinder = 2πrh; sphere = 4πr².
Worked example: A cylindrical water tank has radius 1.5 m and height 2 m. Find its capacity in litres. (Take π = 3.14.)
V = 3.14 × 1.5² × 2 = 14.13 m³
14.13 m³ × 1000 = 14 130 litres
Worked example: Find the area of a sector of radius 7 cm and angle 72°. (Take π = 22/7.)
Area = 72/360 × 22/7 × 7² = 30.8 cm²
Exam tip: Convert all lengths to the same unit BEFORE calculating areas or volumes.
Check yourself
- Find the area of a trapezium with parallel sides 8 cm and 12 cm and height 5 cm.
- A cone has radius 3 cm and height 4 cm. Find its volume, leaving π in the answer.
- Convert 2.5 m² to cm².
Show answers
- 50 cm²
- 12π cm³
- 25 000 cm²
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