The rotator is two cones. Let me introduce the cone lateral area formula: s = π * r * l.

Where π is π, R is the bottom radius, and L is the bus length (AC, BC in the figure).

In this way, we only need to know the radius of the bottom surface.

It is easy to know that the length of AB is 25cm, so the bottom radius is r= 15*20/25= 12cm.

So the total area of this rotating body is

s =π* r *(AC+AB)= 420πcm ^ 2。 Please note that I didn't bring π in.