An arc of a parabola has parametric equations $x=at^2$, $y=2at$ for $0\leq t \leq p$
(i) Find, in terms of $a$ and $p$, the area of the surface of revolution formed when this arc is rotated about the x-axis through $2\pi$ radians.
(ii) Find an approximation to this surface area when $p$ is sufficiently small for powers above $p^2$ to be ignored. Interpret this approximate area geometrically.
Regarding the last part of (ii), the answer is $4\pi a^2p^2$ which I interpreted as the area of a circle with radius $2ap$. Not sure if my interpretation is fine. Is there any other ways to describe the approximate area?