Correct Measurement of Length

Measurement  of Area
The amount of surface covered by the object is called its area. The measurement of area counts two dimensions. The SI unit of area is square metre, represented as m². This is the area covered by a square whose length and breadth are 1 m each. 

The area of regular surfaces (squares, rectangles etc.) can be measured by using the following formula: 
area of a square = length × length 
area of a rectangle = length × breadth

Ex.1    How many m²  are equal to 1 cm² area?
Sol.     1 m² = 1 m × 1 m 
        = (100) cm × (100) cm
        = (10000) cm² = 104 cm²

Measurement  of volume
The amount of space occupied by an object is its volume. The SI unit of volume is the cubic metre represented as m³ .
The litre (represented as l) is an important unit of volume used in the everyday life.
1 litre = 1000 ml    
1 m³ = 1000 litres
The litre is also known as 1000 cm³.
Since 1 litre = (1/1000) m³.

The volume of a liquid is more often expressed in millilitres. 

The volume of a solid that has a regular shape can be calculated using a mathematical formula. The formula for determining the volumes of some regular solids are: 
Volume of a cube = l³ 
where l is the length of the side of the cube. 
Volume of a cuboid = l × b × h 
where l is the length, b is the breadth, and h is the height of the cuboid. 
e.g.    Volume of a cube of side 1 m 
        = 1m × 1m × 1m 
        = 1 × 1 × 1 m³ 
        = 1 m³ 

Volume of a cube of side 1 cm 
        = 1 cm × 1 cm × 1 cm 
        = 1 × 1 × 1 cm³ 
        = 1 cm³ 
    Volume of a cube with sides 10 cm 
        = 10 × 10 × 10 cm³ = 1000 cm³ 

    Volume of a cube with sides 1 dm 
        = 1 × 1 × 1 dm³ = 1 dm³ 
        1000 cm³ = 1 dm³ 
        1 litre = 1000 ml 
        = 1000 ml 
    or     1 cm³ = 1 ml 

Ex.2    Convert : 
        (i) 54 km/hr = ? m/s                (ii) 15 m/s = ? km/hr    
        (iii) 30 km/cm = ? m/mm        (iv) 12 m/km = ? mm/cm