# L37 Volumes Disk Washer - L37 Volume of Solid of Revolution...

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L37 Volume of Solid of Revolution I Finding the Volume of the Solid of Revolution{Disk/Washer A solid of revolution is a solid obtained by rotating a plane area around some straight line (the axis). Two common methods for nding the volume of a solid of revolution are the disk method and the shell method of integration. To apply these methods, it is easiest to: 1. Draw the graph in question; 2. Identify the area that is to be revolved about the axis of revolution; 3. Determine the volume of either a disk-shaped slice or a cylindrical shell of the solid; 4. Integrate all the in nitely many disks or shells . 1
Disk method The volume V of the solid formed by rotating a plane area about the x axis is given by V = Z b a A ( x ) dx = Z b a f 2 ( x ) dx and about the y axis by V = Z b a A ( y ) dy = Z b a g 2 ( y ) dy where A ( x ) and A ( y ) is the cross-sectional area of the solid. 2
ex. Find the volume of the solid generated when the area bounded by the curve y = p x , the x axis and the line x = 2 is revolved about the x axis.