Consider a certain steel sample of eutectoid composition $(0\mathrm{.}76wt\%$ Carbon$).900C$ down to room temperature, the sample undergoes an allotropic transition from the face centered cubic Austenite structure to the body centered cubic ferrite structure and the. orthorhombic cementite structure. Note that, since the carbon exists at the interstitial sites of the carbon lattice, the crystal structures referenced above refer to the iron crystal structures. For your reference, the phase diagram is shown below.

$\frac{g}{c}{m}^3$

b$.$ If it is assumed that the ferrite structure contains approximately zero carbon at room temperature, what is the theoretical density of this ferrite structure?

c$.$ If the total sample density remains constant through the allotropic transition, what is the estimated density of the cementite structure.