The flux is directly proportional to the area of the loop. You don't need the cos theta part in your formula since we are told the magnetic field is perpendicular to the area of the loop. The area is that of a circle, and it is a function of time:
[tex]\Phi_B = BA= B\pi r^2(t)=B\pi(r_0+bt)^2[/tex]
The last form answers 6a.
The induced electromotive force (EMF) is the negative change of the flux, so you can use a derivative to answer the question 6b:
[tex]EMF=-\frac{d\Phi_b}{dt}=\frac{d}{dt}[-(B\pi(r_0+bt)^2]=-2B\pi b(r_0+bt)[/tex]
(b is treated as a constant, so there is no need to differentiate it). As you can see, the EMF is linear in time, and quadratic in b.
