**Mensuration Formulas for O-Level E Math**

Dive into our list of Mensuration Formulas, to make sure you can solve Mensuration problems with ease in your O-Levels E-Math papers with this formula sheet.

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**Perimeter**

1. We use **millimetres** (mm), **centimetres** (cm), **metres** (m) and **kilometres** (km) as units for measuring lengths or distances.

The units are related as follows:

1km = 1000m; 1m = 100cm; 1cm = 10mm

2. Perimeter of a **circle** is referred to as the circumference. The **circumference**, *C*, of a circle of radius, r, can be obtained by using this formula, circumference = 2 × π × *r* where π = 3.14 or ^{22}⁄_{7}.

**Area**

3. Area of a closed figure is the amount of space it covers. It is measured in square units.

4. Note:

a) 1 cm^{2} = 1 cm × 1 cm

= 10 mm × 10 mm

= 100 mm^{2}

^{ }

b) 1 m^{2} = 1 m × 1 m

= 100 cm × 100 cm

= 10 000 cm^{2}

c) 1 km^{2} = 1 km × 1 km

= 1 000 m × 1 000 m

= 1 000 000 m^{2}

Hectare (ha) is a unit for measuring large land areas such as farms.

1 ha = 10 000 m^{2}

5. Area of a **triangle** = ^{1}⁄_{2} × base × height

6. Area of a **parallelogram** = base × height

7. Area of a **trapezium** = ^{1}⁄_{2} × (sum of parallel sides) × height

8. Area of a **circle** = π × *r ^{2}*, where π = 3.14 or

^{22}⁄

_{7}.

**Volume**

Volume of an object is the amount of space it occupies. We use cubic metre (m^{3}), cubic centimetre (cm^{3}) and millimetre (mm^{3}) as units for measuring volumes.

9. Note:

a) 1 cm^{3} = 1 cm × 1 cm × 1 cm

= 10 mm × 10 mm × 10 mm

= 1000 mm^{3}

^{ }

b) 1 m^{3} = 1 m × 1 m × 1 m

= 100 cm × 100 cm × 100 cm

= 1 000 000 cm^{3}

c) 1 km^{3} = 1 km × 1 km × 1 km

= 1 000 m × 1 000 m × 1 000 m

= 1 000 000 000 m^{3}

10. Volume of a **cuboid** = length × breadth × height

11. Volume of a **cube** = length × length × length

12. A cylinder is a special prism with a circular cross-section. Hence, its volume can be found by multiplying the area of the circular base by its height.

Volume of cylinder = Πr^{2}h

**Surface Area**

13. A cube has 6 equal faces. Therefore, its surface area is obtained by multiplying the area of one face by 6.

14.The lateral surface of a cylinder is also called the curved surface. If we rolled up a piece of rectangular sheet, the rectangular sheet will become the curved surface of the cylinder.

Area of rectangle = curved surface area of the cylinder

= *2πrh*

Hence, total surface area of a solid cylinder = area of curved surface + 2 × area of base

= *2πrh + 2πr ^{2}*

**Volume and Surface Area of a Pyramid**

A pyramid is a solid that has a base with a perpendicular vertex and slant lateral faces.

The base can be any polygon with 3 sides or more (triangle, a square, or a rectangle, etc.)

Volume of pyramid = ^{1}⁄_{3} × base area × height *Base area = *s²* *

Surface area of 4 sides = ^{1}⁄_{2} × s × *l *× 4 sides

= 2s*l *

Surface area of pyramid = ^{1}⁄_{2} × base area + total area of slant ∆ faces

= s^{2} + 2s*l *

**Volume and Surface Area of a Cone**

A cone is a solid with a circular base and a vertex.

Arc length = circumference of circular base

Curved surface area of cone = πr*l*

Volume of cone = ^{1}⁄_{3}πr^{2 }

Surface area of a cone

= Area of circle + Area of curved surface

= πr^{2} + πr*l*

*r *= radius

*l* = length of slant height =√(r^{2}+h^{2})

**Volume and Surface Area of a Sphere and Hemisphere (Half-Sphere)**

Every point on the surface of a sphere is equidistance from the centre.

A hemisphere is half a sphere.

Volume of sphere = ^{4}⁄_{3}πr^{3 }

Surface area of a sphere = 4πr^{2 }

Volume of hemisphere = ^{1}⁄_{2} × volume of sphere = ^{2}⁄_{3}πr^{3 }

Surface area = ^{1}⁄_{2} × spherical surface area + area of circle

= 2πr^{2}+ πr^{2 }= 3πr^{2}

**Volume and Surface Area of a Prism**

Volume of prism = Base area × Height

Or Area of cross-section × Length

Surface area of a prism = Area of all the faces

Or 2 × Cross-Sectional Area + (Perimeter of Cross Section) × length of prism

Volume of triangular prism = ^{1}⁄_{2 }×* b × h × l*

**Radian Measure**

Radian is another unit of measure for angles, similar to degrees.

One radian is the angle made at the center of a circle by an arc whose length is equal to the radius of the circle.

**Conversion from radians and degrees**

2π *radians* = 360°

π *radians* = ^{360°}⁄_{2} = 180°

1 *radian* = ^{180°}⁄_{π}

**Conversion from degree to radians**

360°= 2π *radians *

180° = π *radians*

1°= ^{π}⁄_{180} rad

**Conversion between radians and degrees**

**Part of a Circle**

**Arc Length**

If θ is measured in degree then arc length = ^{θ°}⁄_{360° }_{× 2πr}

If θ is measured in radian then arc length = ^{θ°}⁄_{2π}_{ }_{× 2πr = rθ}

**Area of Sector **

Area of circle = πr²

If θ is measured in degree then area of sector = ^{θ°}⁄_{360}_{ }_{× πr² = rθ}

If θ is measured in radian then area of sector = ^{θ°}⁄_{2π}_{ }_{× πr² = }^{1}⁄_{2 r²θ}

**Area of Segment**

Area of segment = Area of Sector ‒ Area of Triangle

= ^{θ°}⁄_{360° }× πr² ‒ ^{1}⁄_{2} r² s*in*θ (if θ is a degree)

= ^{1}⁄_{2 }r²θ ‒^{1}⁄_{2 }r²s*in*θ (if θ is a radian)

Important: If angles are in radian, change the calculator to radian mode.

For more mensuration formulas and tips, check out our free math eBooks and test papers for secondary school students!

## Last Minute Revision for O Level Math?

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**Before you go, you might want to download this entire formula sheet in PDF format to print it out, or to read it later. **

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NIE Trained

Math Specialist

Jimmy Maths and Grade Solution Learning Centre

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