Let S be a sphere of radius R, center at the origin and let C be a cylinder of radius r (r < R) with the z-axis the axis of rotation. We are concerned with the volume of the part of S outside C. This cored sphere can also be realized by taking the region bounded by the circle
x and the line
h = R Hence the area of the washer is
Area = p[(R The smallest y value the cross-section will have is -h and the largest is h. We can write this as an integral Notice that the volume only depends on the height of the region. |