The concept of rotating a circle around the X/Y axis using cylindrical shells is based on the method of finding the volume of a solid object formed by rotating a two-dimensional shape around an axis. This method involves slicing the shape into cylindrical shells and then summing up the volumes of each shell to get the total volume of the solid object.
The radius of the cylindrical shells is determined by the distance between the axis of rotation and the outer edge of the shape. This distance remains constant for all the shells and is equal to the radius of the original circle.
The formula for finding the volume of a single cylindrical shell is V = 2πrhΔx, where r is the radius of the shell, h is the height of the shell, and Δx is the width of the shell.
The number of cylindrical shells needed for accurate volume calculation depends on the desired level of accuracy. Generally, the more shells used, the more accurate the volume calculation will be. It is recommended to use a large number of thin shells for a more accurate result.
Yes, the method of using cylindrical shells can be applied to other shapes besides circles. It can be used for any two-dimensional shape that can be rotated around an axis to form a solid object. The shape just needs to be sliced into cylindrical shells and the volume of each shell can be calculated and summed up to get the total volume of the solid object.