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 $1$ Kg 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 $0\mathrm{.}4$ kg per kg of pig iron and is containing pure Calcium carbonate. The blast furnace gas has $30\%$ CO and $15\%$ CO$2.$ Considering the base of one tonne of pig iron produced, calculate the following assuming the necessary data required:

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$1.$ The weight of core used.

$2.$ The weight of slag made.

$3.$ The volume of the blast$-$furnace gas.