solve for the lateral surface area

Question

Find the lateral surface area of the cone generated by revolving the line segment ,  about the 

Answer 1

You can use calculus to get this answer, but I would suggest it can be done this way.

If you cut the cone through the vertex and flatten it out, it will be a circle with radius of

sqrt[2²+(1/3)²]. And the surface area you want is simply the area of the circle.