How is iron extracted from haematite?

Hint: Haematite is an oxide ore of iron. The steps of extraction of iron are the concentration of ore, calcination, and smelting. The calcined ore is reduced with carbon.

Complete answer:
Iron is usually extracted from the oxide ore (haematite). It involves the following steps:
Concentration: The ore is crushed in jaw crushers and the crushed ore is concentrated by the gravity separation process in which the crushed ore is washed in a stream of water when lighter sand and clay particles are washed away while the heavier ore particles settle down. In the case of sulfide ore concentration is carried out by the froth flotation process.
Calcination: The concentrated ore is then calcined i.e., heated strongly in the presence of a limited supply of air in a reverberatory furnace. During calcination, the following changes occur.
i)- Moisture is removed
ii)- Impurities of sulfur, phosphorus, and arsenic escape as their volatile oxides.
$\begin{align}
  & {{S}_{8}}+8{{O}_{2}}\to 8S{{O}_{2}}\uparrow \\
 & {{P}_{4}}+5{{O}_{2}}\to {{P}_{4}}{{O}_{10}}\uparrow \\
 & 2As+5{{O}_{2}}\to A{{s}_{2}}{{O}_{5}}\uparrow \\
\end{align}$
iii)- Ferrous oxide is oxidized to ferric oxide thereby preventing the loss of iron as slag during melting.
$4FeO(s)+{{O}_{2}}(g)\to 2F{{e}_{2}}{{O}_{3}}(s)$
iv)- The ore becomes porous and hence is more suitable for reduction to the metallic state.
$\begin{align}
  & FeC{{O}_{3}}(s)\to FeO(s)+C{{O}_{2}}(g) \\
 & 4FeO(s)+{{O}_{2}}\to 2F{{e}_{2}}{{O}_{3}}(s) \\
\end{align}$
Smelting:Carbon is used to reduce the calcined ore i.e. smelted in a blast furnace. It is a tall cylindrical furnace made of steel and lined inside with fire bricks.
The charge consisting of calcined ore, coke, and limestone is introduced into the furnace from the top through cup and cone arrangement. At the same time, a blast of hot air preheated to about 1000K is blown into the furnace through tuyeres. The added coke serves both as a fuel as well as a reducing agent while added limestone acts as a basic flux.
The reaction is:
$FeO(s)+C(s)\to Fe(s)+CO(g)$

Note:
The final reduction of iron oxide with carbon is a redox reaction. The iron oxide is reduced to iron metal and the carbon is oxidized to carbon dioxide.