Say given a semi-circle, the region is boudned by the x axis, and a solid of revolution is formed by rotation across the y axis. Then a solid of revolution is formed using also the given semi circle but bounded by both the x-axis and y-axis, and then rotated across the y axis. What is the difference in area?

Since by visualising the solid formed, there wouldnt be a difference since the solid formed is the same. IS that correct? Or am i visuallising something wrong?