I'm not sure if linear approximations are the way to go here. we want to use differentials, slightly different thing.

60 m = 6000 cm

so our diameter is 6000cm, so the radius is 3000cm

the amount of paint is talking about the volume. so the radius is 3000 cm and we want a coat of paint 0.02 cm thick, so the error in radius or the change in radius is dr = 3000.02 - 3000 = 0.02