Question $1($Shaft sinking$)$

A $9$ diameter shaft is being sunk through a rock with a $($true$)$ density of $2\mathrm{.}7\frac{t}{m^3}$ with swell factor of $15\%$ at a rate of $6m$ per day. The shaft is equipped with kibbles that have $2m$ diameter and are $2m$ high $($internal measurements$).$

$1\mathrm{.}1$ What tonnage of rock must be cleared each day?

$(3)$

$1\mathrm{.}2$ How many kibble loads must be hoisted to surface each day to remove the broken rock if a kibble has a fill factor of $80\%?$

$(4)$

$\mathrm{.}3$ You are told that there are two shifts per day working at the mine, with a $3m$ advance per shift required to achieve a $6m$ daily advance. The mine operates at two $12-$hour cycles and the allocated cleaning time per shift is $6$ hours. Assess and conclude whether the cleaning activity will be completed by the required time:

One kibble is hoisted per trip.

The total cycle time per trip $($from shaft bottom to surface, then back to shaft bottom$)$ is $6$ minutes.

A $0\mathrm{.}85m^3$ Cactus grab loading period.

The loading$/$lashing cycle time of a cactus grab per load is $0\mathrm{.}7$ minutes.

$(12)$