If slices perpendicular to the y-axis are semi-circles, we have another loaf of French bread. The radius of the semi-circle at height y is x, where x is the distance from the line x = 0 to the curve x2 + y2 = 1.
Rearranging the equation, we get
The area of the semi-circle at height y is
so the volume of the slice is
The variable y goes from -1 to 1 in the region R, so the volume of the solid is
Alternately, since the solid is symmetric we could find the volume of its upper half and then multiply by 2. his gives us the expression