Volume by shells is a method of finding the volume of a solid of revolution. This method involves splitting the shape into indefinitely small rectangles folded into a cylinder shape. The formula for the volume of any solid of rotation is , where is an area function. This can be applied to any axis of rotation. In the case of volume by rings, the formula is
assuming the rotation is around the -axis.
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To find the volume of the resulting solid when is rotated around the -axis on the interval , one must first solve the equation for . This gives . The interval must then be changed into an interval of , giving . Now it can be substituted into the formula.