Lead melts at $327C$ and tin melts at $232C.$ They form a eutectic containing $62$ percent tin at $182C.$ The maximum solid solubility of tin in lead at this temperature is $19$ percent; of lead in tin, $3$ percent. Assume the solubility of each at room temperature is $1$ percent.

$($a$)$ Draw the equilibrium diagram to scale on a piece of graph paper and label it completely.

$($b$)$ For an alloy containing $40$ percent tin, $($i$)$ give the chemical composition and relative amounts of the phases present at room temperature, $($ii$)$ show the major microstructural changes that occur during slow cooling of the alloy from its liquid state, and $($iii$)$ draw the cooling curve.