I'm afraid your total surface area, A, is lacking.

The problems asks us to find dV/dr in terms of A.

V = pi(r^2)h = pi(r^2)(2r) = 2pi(r^3)

A = 2[pi(r^2)] +2pi(r)*h

A = 2pi(r^2) +2pi(r)(2r)

A = 2pi(r^2) +4pi(r^2)

A = 6pi(r^2)

So,

V = 2pi(r^3)

= [pi(r^2)](2r)

= [A/6](2r)

= (1/3)A*r

Differentiate that with respect to r,

dV/dr = (1/3)A ----------------------------answer.