The area of a circle can written as:
A=πr2
If we take the derivative of both sides with respect to time,
dtdA=πdtd(r2)
dtdA=π⋅2r⋅dtdr
dtdA=2πrdtdr
The question mentions that the rate that the area is increasing is 4 times that of the radius:
dtdA=4dtdr
Substituting this into the equation we found earlier,
4dtdr=2πrdtdr
π2=r