Mensuration
Mensuration measures shapes. Sketch how a composite shape can be split into familiar parts and decide whether the question asks for a boundary, a surface or the space inside. Only exposed faces count towards external surface area.
What this guide covers
Perimeter, area, surface area and volume, including composite figures, arcs, sectors, segments and radians. Keep length, area and volume units distinct.
Syllabus reference: 2026 Mathematics 4052, G5, page 9. These are Mentora search groupings, not new official syllabus categories.
Worked example
Find the volume and total surface area of a closed cylinder of radius 3 cm and height 8 cm, in terms of π.
Volume = πr²h = π × 9 × 8 = 72π cm³. Total surface area includes two circles and the curved surface: 2πr² + 2πrh = 18π + 48π = 66π cm².
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
A trapezium has parallel sides 6 cm and 10 cm and perpendicular height 5 cm. Find its area.
Show worked answer
Area = ½(6 + 10) × 5 = 40 cm². Use the perpendicular height, not a sloping side.
Check 2
Convert 0.35 m² to cm².
Show worked answer
1 m² = 100² cm² = 10 000 cm². Thus 0.35 m² = 3500 cm².
Check 3
Find the area of a sector of radius 6 cm and angle π/3 radians.
Show worked answer
With the angle in radians, area = ½r²θ = ½ × 36 × π/3 = 6π cm².
Common mistakes to watch for
- Surface area uses square units and volume uses cubic units.
- Do not count a hidden joined face in the external surface area of a composite solid.
- The formula ½r²θ requires radians; for degrees use θ/360 × πr².
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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More G3 Math topicsPublished by Mentora · Sources checked 11 Sept 2026
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