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Topic: Solid of revolution

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  Solid of revolution - Wikipedia, the free encyclopedia
In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis) that lies on the same plane.
Assuming that the figure lies entirely on one side of the axis, the solid's volume is equal to the length of the circle described by the figure's barycenter, times the figure's area.
A representative disk is three-dimensional volume element of a solid of revolution.
en.wikipedia.org /wiki/Solid_of_revolution   (621 words)

 The Washer Method for Solids of Revolution   (Site not responding. Last check: 2007-11-05)
If we slice the solid perpendicular to the axis of revolution as in Figure 2, the resulting solid resembles a washer, hence the technique for calculating the volume of the solid of revolution is called the washer method.
Note that the washer is sliced perpendicular to the hole (axis of revolution) while the orientation of the shell is parallel to the hole (axis of revolution).
For a solid of revolution generated by revolving a region about the y-axis, the inner and outer radii are functions of y.
mathdemos.gcsu.edu /washermethod   (1280 words)

 Visualizations for Volumes of Solids in Calculus   (Site not responding. Last check: 2007-11-05)
Rather than introduce volumes of solids of revolution by a purely formula-driven approach, these demos provide the opportunity for visualization of the basic approximating elements that lead to the standard calculus expressions that, when computed, give the desired volumes.
We tell students that we can cut the solid into pieces that have a known cross section or, in the case of solids of revolution, we dissect the surface of revolution into "disks", "washers," or "cylindrical shells".
Solids of Revolution: The Method of Shells involves revolving a region bounded by a curve y = f(x) and the domain interval [a,b] about the y-axis.
mathdemos.gcsu.edu /solids   (972 words)

 MSN Encarta - Search Results - solid of revolution
If emerging economies have to relive the entire industrial revolution with all its waste, its energy use, and its pollution, I think it's all over.
Solid, the physical state of matter in which samples maintain their shape and size.
Solid (geometry), three-dimensional figure along with the volume it encloses.
ca.encarta.msn.com /solid_of_revolution.html   (153 words)

 Solids of Revolution
The purpose of this lab is to use Maple to study solids of revolution.
Solids of revolution are created by rotating curves in the x-y plane about an axis, generating a three dimensional object.
Plot the solid of revolution obtained by revolving the graph of this function around the x axis.
www.math.wpi.edu /Course_Materials/MA1022A99/volumes/node1.html   (982 words)

 Vision system for analyzing solid-of-revolution radius profile - Patent 5918196
The resulting parts are referred to as "solids of revolution." Examples include a clay pot produced on a rotating wheel, a baseball bat shaped on a lathe, or a silicon crystal grown from a rotating seed dipped into a silicon melt.
A common non-contact approach for gauging parts described as solids of revolution involves viewing the object with a camera whose line-of-sight is normal to the object's axis of revolution.
Repeating such measurements at many locations along the full length of the solid of revolution, one generally obtains a radius profile as in the case of the general radial profile inspection system, or a time-varying radius and melt level of a semiconductor crystal, as in the specialized case of a crystal growth inspection system.
www.freepatentsonline.com /5918196.html   (6104 words)

 Generalized Solids of Revolution
There is one axis and one curve on the input side and one solid of revolution on the output side.
Segment is threatened as standalone generalized solid of revolution for purposes of slice creation.
Detailed description how to model shell (but using special version of generalized solid of revolution rather than segments) is given in chapter 6.
www.cg.tuwien.ac.at /studentwork/CESCG/CESCG-2002/PCech/chapter_2.html   (848 words)

 Disk Method   (Site not responding. Last check: 2007-11-05)
A vase created on a potter's wheel is a nice example of solid of revolution generated by rotation about a vertical axis.
The solid generated by revolution by the region R in Figure 8 looks like a cucumber; see Figure 10.
The disks are cylinders which approximate the volume of the actual slices of the solid generated by the revolution of region R. Figure 14 shows a curve and then one strip of area which generates the cylindrical disk displayed in Figure 15.
astro.ocis.temple.edu /~dhill001/diskmethod/diskmethod.html   (1313 words)

 Sandia Joins Revolution In Solid-State Lighting   (Site not responding. Last check: 2007-11-05)
Sandia National Laboratories is among the research entities around the country at the forefront of the revolution.
In some applications they also enable significant cost savings due to their lower consumption of energy: LED-based red traffic lights, for example, consume one-tenth the energy of their incandescent counterparts, enabling them to pay for themselves in as little as one year.
Researchers believe that the development and adoption of solid state lighting technology could reduce the nation's electrical consumption by 10 percent.
www.pinian.com /revolution_in_solid_state_lighting.html   (635 words)

 4.8 Volumes of Solids of Revolution
In this section, the Riemann Sum approach is used to develop an integral formula for the volume of a solid of revolution.
On-screen applet instructions: The applet depicts approximating the volume of a solid of revolution with a finite number n of disks.
Find the volume of the solid generated by rotating the region bounded by y = x, y = 3 – x, and x = 4 around the line x = 5.
www.math.dartmouth.edu /~klbooksite/4.08/408.html   (311 words)

You can create a solid of revolution as you did in your Portfolio Activity by using several copies of a shape.
This interactive site illustrates the solid of revolution created by rotating the graph of a function about the x-axis.
This interactive site plots a solid of revolution generated by rotating the graph of y=f(x) in the interval [a,b] about the x- or y-axis.
go.hrw.com /hrw.nd/gohrw_rls1/pKeywordResults?MG1+SolRev   (153 words)

 [No title]   (Site not responding. Last check: 2007-11-05)
Volume of a Solid of Revolution: Computing the volume of a solid of revolution =  EMBED Equation.3 , where h = height of the solid.
Find the volume of the solid of revolution formed by rotating about the x-axis the area bounded by f(x) = e x, y = 0, x = 1 and x = 3.
Find the volume of the solid of revolution formed by rotating about the x-axis the area bounded by g(x) = 4 - x2 and the x-axis.
instruct1.cit.cornell.edu /Courses/math006/handouts/Handout10.doc   (586 words)

 SparkNotes: Applications of the Integral: Volumes of Solids
The application of integrals to the computation of areas in the plane can be extended to the computation of certain volumes in space, namely those of solids of revolution.
The shell method is applied to a solid obtained by revolving the region below the graph of a function f (x) from a to b about the y-axis.
Even when the cross-section is not a disk (as it is in the case of more general solids of revolution), there may still be a function A(x) that gives the area of the cross section obtained by slicing the solid with the plane through x and perpendicular to the x-axis.
sparknotes.com /math/calcbc2/applicationsoftheintegral/section2.rhtml   (618 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-11-05)
Date: 05/21/2001 at 09:32:13 From: Stan Winston Subject: Alternate Surface Area of Solid of Revolution Formula My teacher mentioned that we were going to be looking at surface areas of solids of revolution shortly after we did volumes of rotation.
When the multiple circumferences are accumulated by integration, it's the same as adding the areas of multiple cylindrical strips with infinitely small widths, which should give me the surface area.
In fact, the only solid that I've found my formula to work for is the cylinder.
mathforum.org /library/drmath/view/51814.html   (828 words)

For the following, you may use either the disk method or the shell method to find the volumes of the solids of revolution.
For each of the following: (i) graph the function and adjust the viewing rectangle to show the graph only on the given interval; (ii) graph the solid of revolution obtained when the function restricted to the given interval is revolved about the
For each of the following: (i) graph the solid of revolution obtained when the function restricted to the given interval is revolved about the
www.csun.edu /~kme52026/s4b3/s4b3.htm   (206 words)

 Solid of Revolution   (Site not responding. Last check: 2007-11-05)
A solid of revolution S is one obtained by:
Hence the volume of a solid of revolution is:
The diagram demonstrates this formula, and why it is called the disk method.
pear.math.pitt.edu /Calculus2/week6/6_1li5.html   (77 words)

 How to calculate the volumes of these solids   (Site not responding. Last check: 2007-11-05)
Where a and b are the locations of the left bound and the right bound of the solid on the x-axis.
Where c and d are the locations of the lower bound and the upper bound of the solid on the y-axis.
Following the same approach as the previous case we can get the volume of a solid of revolution by revolving a curve described by f(y) about an axis parallel to the y-axis that is described by g(y).
www.iitap.iastate.edu /calc/khabiry/Calculus/math166/Sec6_2/module_3.htm   (347 words)

 Calculus I (Math 2413) - Applications of Integrals - Volumes of Solids of Revolution / Method of Rings   (Site not responding. Last check: 2007-11-05)
In the final section of the Extras chapter we derived the following formulas for the volume of this solid.
A(y) is the cross-sectional area of the solid.  There are many ways to get the cross-sectional area and whether we will use A(x) or A(y) will depend upon the method and the axis of rotation used for each problem.
There is a portion of the bounding region that is in the third quadrant as well, but we don't want that for this problem.
tutorial.math.lamar.edu /AllBrowsers/2413/VolumeWithRings.asp   (1121 words)

axis as well as the solid for which you wish to compute the volume.
You can think of solids of revolution as using a certain amount of surface area to enclose a certain amount of volume.
Evaluate the volumes of the solids in problems 1, 2, and 3 and record the results in the table below.
www.csun.edu /~kme52026/f3b2/f3b2.htm   (357 words)

 Maxfli Revolution Solid Golf Balls
Revolution Solid ball combines the added distance of solid balls with exceptional feel
Enclose original cash register receipt for purchase and the original UPC bar code cut out from a Maxfli Revolution Solid package of one dozen golf balls (UPC bar code from left side of box).
Limit one free glove per box of one dozen Maxfli Revolution Solid golf balls purchased.
www.golfstockpile.com /index.asp?PageAction=VIEWPROD&ProdID=909   (261 words)

 The Origin Forum - Revolution solid
I was wondering if there was any way to generate a revolution solid in Origin.
That said, it may be possible to generate a 3D solid by glueing together two halves.
For a "revolution solid", it would be more complicated.
www.originlab.com /forum/topic.asp?TOPIC_ID=3693   (316 words)

 Solid of Revolution - The Shell Method
In addition to the disc or washer method of finding volumes of revolution, a popular method is the Shell Method.
The length is the circumference of the circular shell.
The formula for the volume of such a solid is:
users.rcn.com /mwhitney.massed/shell_method/shell_method.html   (252 words)

 Sandia joins revolution in solid-state lighting
ALBUQUERQUE, N.M. - A revolution is quietly occurring that promises to change the way we light our homes, offices, and world.
Some 25 Sandia researchers are working on an project that will establish the fundamental science and technology base to replace the country's primary lighting source, incandescent bulbs and fluorescent tubes, with semiconductor light-emitting diodes (LEDs) - solid state lighting.
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin company, for the U.S. Department of Energy.
www.eurekalert.org /pub_releases/2002-04/dnl-sjr041602.php   (732 words)

  Surface Area of a Solid of Revolution Around an Oblique Axis where the Sides of the Region are Perpendicular to the Same Axis.
S be the surface area of the solid obtained by rotating this region around
 corresponds to the radius of the solid of revolution.
www.selu.edu /Academics/Depts/Math/students/milton/milton.htm   (1356 words)

 rgenkou   (Site not responding. Last check: 2007-11-05)
"Animate" button shows the revolution of the original figure about the x-axis.
It shows the solid of revolution and a cross-section.
The volume of the solid is approximated by computing the sum of the volume of disks.
www.ies.co.jp /math/java/calc/rotate/rotate.html   (57 words)

 Polyhedrons & Solid of revolution
One of the hardest section in geometry is drawing the faces of a solid figure on plane and in this section we will show you how to build these shapes and how to draw the faces of that shapes on plane.
The polyhedron is a solid bounded by plane polygons.The bounding polygons are the faces, the intersection of the edges, and the points where three or more edges intersect are the the vertices of a polyhedron.
But the areas will be different because of its lateral faces which have different figure.
math.schoolnet.ir /english/contents/S_Geo/shape1.html   (161 words)

 Maxfli Revolution solid??? - Golf Rewind
I should have known that i would get what i payed for but several years ago the maxfli rev was a nice ball with a solf cover, then they came out with a rev solid that was sopossed to compete with the pro v.
I saw this "new" rev solid and at such a deal grabbed them but the are really really bad, just like a top rock, they have a hard plasticky cover and are like putting rocks.
They are the same Rev Solid balls that were a disappointment when they first came out.
www.golfrewind.com /showthread.php?p=159437#post159437   (321 words)

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