L11 - Volume Calculation by the Method of Rotation

L11 - Volume Calculation by the Method of Rotation -...

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Volume By Rotation (Section 6.1) The volume of a slice is the area of the slice multiplied by the width of the slice. V i = (area of side of slice i )(width i ). The total volume is then: V A ( x ) dx a b or V A ( y ) dy c d . We are going to examine slice perpendicular to an axis of revolution. When we revolve the slices, we get disks or washers depending on the initial region. Always make slices perpendicular to axis of revolution. Always integrate along the axis perpendicular to a slice. DEF The Disk Method T volume of a solid of revolution whose cross-sections are circular disks of radius R(x) is V A ( x ) dx a b [ R ( x )] 2 dx a b
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