Tuesday, 14 September 2021 09:00

# General Mathematics Formulae - Class 8 Mathematics Revision Notes

## Length

The units of length that are used include the following:

• millimetre (mm)
• centimetre (cm)
• decimetre (dm)
• Metre (m)
• Dekametre (Dm)
• Hectometre (Hm)
• Kilometre (Km)

From the illustration:

• 10mm = 1cm
• 10cm = 1dm
• 10dm = 1m
• 10m = 1 Dm
• 10Dm = 1Hm
• 10 Hm = 1Km

The relationship between the units of lengths may be clearly seen if the units are written with a 10 between them.

So to find how many small units are equivalent to another, multiply the number of tens between the units, hence:

• Km 1
• Hm 10
• Dm 100
• M 1000
• dm 10000
• mm 1000000

## Mass

• 1000 g = 1Kg
• 1000 Kg = 1Tonne
• 1000000 g = 1Tonne

## Volume and Capacity

• 1 cm3 = 1 Ml (millilitre)
• 1000 cm3 = 1 L (litre)
• 100 cm3 = 1 dl (decilitre)
• 1 m3 = 1000 litre
• 1000000 cm3 = 1 m3
• 10 dl = 1 Litre
• 1000ml = 1 Litre

## Time

• 60 Seconds = 1 Minute
• 60 Minutes = 1Hour
• 3600 Seconds = 1 Hour
• 24 Hours = 1 day
• 7 Days = 1 Week

## Area

### Rectangle

Area = Length x Width
A = L X W

### Square

Area = Side x Side
A = S x S
A = S2

### Parallelogram

A = base x Height
A = b x h

### Rhombus

Area = base x height
A = b x h

### Triangle

Area = base x height
A = b x h

### Trapezium

Area = x sum of parallel lines x height
A = (a + b) x h
A = h (a + b)

### Circle, half circle, quarter circle

A = П x r x r

A = Пr2

#### Half circle

Area = Area of a full circle ÷ 2

A = П r2
2

A =½ Пr2

#### Quarter circle

A = Area of the full circle ÷ 4

A = Пr2 ÷ 4

A = ¼Пr2

Note: П = 22/7 or 3.14 or 3 1/7

## Surface Area

### Surface Area of  a Cylinder

T.S.A = Area of circular ends + area of the curved surface

=2Пr2 + Пdh ( if closed both ends)

T.S.A = Пr2 + Пdh (if open one end )

T.S.A = Пdh (if open both ends/pipe)

### Surface Area of  a Cube

T.S.A = Total area of all the six faces

= 6 x L x L

= 6L2 (if closed)

or

= 5L2 (if open one end)

### Surface Area of  a Cuboid

T.S.A = Total area for the six faces

= 2 (L x w) + 2 (L x h) + 2 (w x h)

or

= (L x w) + 2 (L x h) + 2(w x h) ( if open on top)

### Surface Area of  a Triangular prism

T.S.A = Area of all the 5 faces of the prism

## Volume of Cylinder and Rectangular Shapes

### Volume of a Cylinder

Volume = Base area x height

= Пr2 x height

= Пr2h

### Volume of a Rectangular shape

Volume = Base area x height

V = L x w x h

Note: Depending on the cross-section, the volume of any shape / solid is given by.

V = Area of cross-section x height/length

## Perimeter

#### Perimeter of a Rectangle

P = Length + Length + Width + Width

= L + L + W + W

= 2L + 2W or 2(L + W)

#### Perimeter of a Square

P = L + L + L + L

= 4L

#### Perimeter of a Circle

C = П x diameter

= Пd or 2Пr

Note: Perimeter of a full circle is called circumference

#### Perimeter of a Half a Circle

Perimeter = circumference + diameter

P = ½Пd + d

Note: For triangles and irregular shapes, JUST ADD THE DISTANCE ALL ROUND.

## Expressing area of large shape

Hectare – A shape that measures 100m by 100m

Therefore 1ha = (100 x 100)m2

1 ha = 10000m2

Are – a piece / shape that measures 10m by 10m

Therefore 1 are = 10 x 10

1 are = 100m2

Hence:

1 ha = 10000m21are = 100m2

1ha = 100ares