Disk Method - Solids of Revolution The solid generated...

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Solids of Revolution The solid generated by rotating a plan region about an axis in its plan is called a solid of revolution y y .pk [email protected] x x y x x y 3 [email protected]
Disk Method (Rotation about x-axis) The volume of solid of revolution generated by rotating a plan region about x-axis as shown below is y = b a dx x R V ) ( 2 π Disk of radius R(x) .pk [email protected] x x y b a x ) ( x R 4 [email protected]
Example: The region lying in the first quadrant between the curve x=y 2 and lines y=0 and x=4 is revolved about the x-axis to generate a solid. Find its volume. .pk [email protected] 5 [email protected]
x y y ( 29 π ) ( 2 = dx x R V b a 4 0 x ) ( x R x y = x y = Radius of the disk will be x x R = ) ( Volume of the solid of revolution .pk x π π π 8 4 0 4 0 2 = = = xdx dx x Disk of radius R(x) [email protected] 6 [email protected]
Example: The region lying between the curve x=3-y 2 and lines x=3 and y= 3 is revolved about the line y= 3 to generate a solid. Find its volume.