f(x) ba Volumes Using Cylindrical Shells xkxk radius of cylinder height of cylinder circumference of cylinder thickness of cylinder Cross-section is taken parallel to the line of rotation.
Solids of Revolution - Example A solid obtained by revolving a region around a line. Find the volume of a cone of height h and bottom radius r. r h NOTE: Cross-section is parallel to the axis of rotation.
Volumes of Solids of Revolution Comparing Methods Disks & WashersCylindrical Shells Cross-section: Perpendicular to the line of rotation. Cross-section: Parallel to the line of rotation. r is the length of the cross- section in terms of x or y. Rotate about the x-axis: Rotate about the y-axis: h is the length of the cross- section in terms of x or y. Rotate about the x-axis: Rotate about the y-axis: