A section of blood vessel has a flow-rate F in cubic millimetres per
Minute proportional to the fourth power of its radius, R. The blood vessel can be
Considered perfectly cylindrical and is expandable. At some instant the
Flow rate is 30 cubic millimetres per minute when the radius is 0.5 millimetres. At that same instant the flow-rate is increasing at rate of 0.24 cubic millimetres per minute squared.

(I) What is the rate of increase of the radius at that instant?

(ii) If the rate of increase of the radius is constant how long after the time when the
Radius is 0.5 mm is the radius 1 mm?

Can I still use the volume of a cylinder formula? But here it says that the radius can expand and there is no height given?

The problem states

Therefore, since k is constant,

Now, they give

Use the info and the two equations to find k and dR/dt.