It's a little difficult following what you mean - partly because you talk about the "area" of A whereas I think you mean "volume," and also because I don't know what the "a" value is supposed to signify. Is "a" = 0? And when you ask for the value of x, do you mean the value of b to make the two volumes equal?
I will assume that the problem is to find a value for b such that the volume B (which is the defined by rotating y = sqrt(x) about the x axis, and finding the volume from x = 0 to x = b) is equal to the volume A (defined as rotating y = sqtr(x) about the y axis, and finding the volume from y = 0 to y = sqrt(b). If I have that right, then the answer for b turns out to be 6.25. I can help you thorugh this, but before I do please verify that I have interpreted the problem correctly.