Please answer using paper and a pen. Typing will result in VITAL equation syntax missing. A to E please

The rate of dissolution of small drug particles in the body is governed by the rate of mass transport. Since the particle is pure drug, the appropriate expression for the rate of mass transfer is: m=kmA[drugC] where the density of the drug is a constant (drug=1200kg/m3) and C=50kg/m3. The drug particles are assumed to be cylindrical tablets with the mass transfer coefficient given as km=b/R where b=8109m2/s and R is the radius of the cylindrical tablet. A) Write down the transient mass balance describing the change in radius of the cylindrical particle as a function of time. You can assume that the length of the tablet stays constant and that there is no drug dissolution from the ends of the tablet. B) Derive an analytical expression for the particle radius as a function of time. C) How long will it take for the drug particles to disappear if the initial radius of the tablet is 0.005m ? D) Repeat the calculations in parts B and C if the drug is able to dissolve from the ends of the tablet (i.e., if A=Acyliner+Aends ) assuming that L=5R where L is the length of the cylinder. E) Why does it take longer for the drug tablet to dissolve in Part D? The rate of dissolution of small drug particles in the body is governed by the rate of mass transport. Since the particle is pure drug, the appropriate expression for the rate of mass transfer is: m=kmA[drugC] where the density of the drug is a constant (drug=1200kg/m3) and C=50kg/m3. The drug particles are assumed to be cylindrical tablets with the mass transfer coefficient given as km=b/R where b=8109m2/s and R is the radius of the cylindrical tablet. A) Write down the transient mass balance describing the change in radius of the cylindrical particle as a function of time. You can assume that the length of the tablet stays constant and that there is no drug dissolution from the ends of the tablet. B) Derive an analytical expression for the particle radius as a function of time. C) How long will it take for the drug particles to disappear if the initial radius of the tablet is 0.005m ? D) Repeat the calculations in parts B and C if the drug is able to dissolve from the ends of the tablet (i.e., if A=Acyliner+Aends ) assuming that L=5R where L is the length of the cylinder. E) Why does it take longer for the drug tablet to dissolve in Part D