O-Level E-Math and SEC G3 Mathematics K310
G5: Mensuration
Break composite figures into known shapes, keep units consistent, and round only at the final step.
Core notes
Mensuration measures length, area, surface area and volume. Decompose composite figures into standard shapes, preserve units, and distinguish curved surfaces from complete surface area.
Plane and composite figures
Use standard area formulae for parallelograms and trapezia. For a composite plane figure, add required regions or subtract cut-outs. Perimeter follows only the exposed boundary.
Solids and unit conversion
A prism has constant cross-section, so its volume is cross-sectional area times length. For composite solids, add or subtract volumes and surface regions carefully. Since , area conversion uses a factor of and volume conversion uses .
Arcs, sectors and segments
In radians, arc length is and sector area is . A segment area is sector area minus the area of the corresponding triangle for a minor segment.
Formulae and methods
| Relationship | Use |
|---|---|
| Volume of a prism. | |
| Arc length when is in radians. | |
| Sector area when is in radians. | |
| Volume of a cone. | |
| Volume of a sphere. |
Worked examples
Example 1: Find the arc length of a sector with radius and angle radians.
- The angle is already in radians.
- Use .
- Calculate .
Answer: The arc length is .
Example 2: Convert to cubic centimetres.
- Use .
- Cube the conversion factor: .
- Calculate .
Answer: .
Chapter checkpoint
- Sketch and label every required dimension, including hidden radii or slant heights.
- Choose whether the question asks for perimeter, area, surface area, arc length or volume.
- Convert units before combining quantities and round only at the final step.
Exam traps and retrieval check
Avoid these traps
- Using a diameter where the formula requires a radius.
- Applying a linear conversion factor to an area or volume.
- Counting an internal joined face as part of a composite solid's exposed surface area.
Check from memory
How is a minor segment area found?
Subtract the triangle area from the sector area.
What is the area conversion from square metres to square centimetres?
Multiply by .
What must be true before using ?
The angle must be in radians.
Official K310 coverage
This chapter maps to 7 official outcomes: G5.1, G5.2, G5.3, G5.4, G5.5, G5.6, G5.7. Check the official 2027 K310 syllabus for exact assessable wording and paper details.