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 Alluminium 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 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.

$1.$The weight of core used.

$2.$The weight of slag made.

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