A blast furnace makes pig iron containing $3\mathrm{.}2\%$ and $1\mathrm{.}8\%$ of Carbon and Silicon and remaining as Iron respectively. The ore is a combination of $80\%,12\%$ and $8\%$ of Iron Oxide, Silica and Aluminum Oxide respectively. The process requires coke at a rate of $1Kg$ per $kg$ of pig iron produced. The coke is adulterated with Silica with $10\%$ of silica and remaining to be carbon. The flux is obtained at a rate of $0\mathrm{.}4kg$ per $kg$ of pig iron and is containing pure Calcium carbonate. The blast furnace gas has $30\%CO$ and $15\%CO2.$ Considering the base of one tonne of pig iron produced, calculate the following assuming the necessary data required:

$[15]$

The weight of core used.

The weight of slag made.

The volume of the blast$-$furnace gas.