Find the area of the surface formed by revolving the curve a

Find the area of the surface formed by revolving the curve about the specified axis.

Please list out the whole process in detail. I am getting frustrated with half answers and and answers without explanations. Please list out the process in detail so I can learn. Thank you. To help, here is the answer from the answer key:

it forms sphere of radius 1 4*3.14*1^2=12.56