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#WASHERS AND DISK GRAPH SERIES#
If we do that and take slices perpendicular to the axis, we will produce a series of discs (like my watermelon example on this page:) 4. The disc method for finding a volume of a solid of revolution is what we use if we rotate a single curve around the x- (or y-) axis. To apply these methods, it is easiest to: 1.
Two common methods for nding the volume of a solid of revolution are the (cross sectional) disk method and the (layers) of shell method of integration.
#WASHERS AND DISK GRAPH HOW TO#
I don't know how to transform the equation (13) into.
I haven't had calculus in many years but I like to work problems every now. Under the section, "When to use the shell.
URL:Shell Method | Brilliant Math & Science Wiki Nevermind! I ended up being able to solve it mycz, 07:06 Log in Sign up Related Applications of Integration questions Shell Method: Volume of Solid of Revolution Reply Volume of Solid of Revolution (Disk and Washer Methods)Īnd see this page for examples of Shell Method: See this page for explanation and examples of disk and washer methods: You need to use different integration formulas for disks, washers and shells methods. The single washer volume formula is: V (r22 r12) h (f (x)2 g (x)2) dx The exact volume formula arises from taking a limit as the number of slices becomes infinite.
The formula of volume of a washer requires both an outer radius r1 and an inner radius r2. This time we end up with a set of hollow cylinders (something like a water pipe). A washer is the same as a disk but with a center, the hole cut out. The Shell method approaches it from quite a different viewpoint. If we rotate an area between 2 curves, and then take slices, we won't have a discs, instead we'll have washers (like the ones given in the pictures at the top of the page above). If the area bounded by the parabola yx2 and the line yx is revolved about the x-axis, the volume of the solid formed may be found by using which of the following methods A. If we do that and take slices perpendicular to the axis, we will produce a series of discs (like my watermelon example on this page:)Ĥ. Re: Difference between disc method, washer method and shell meth
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