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Volumes and Surface Areas by Simpson's Rule

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FINDINGVOLUMESANDSURFACEAREASOFSURFACESOFREVOLUTIONUSINGSIMPSON'SRULE.ASurfaceofrevolutioncanbeconsideredasasolidofvaryingcrosssection.FindingVolumes:Foreachofanoddnumberofordinates;eachevenlyspaced;wefindtheareaofthecrosssectionandmultiplybythesimpson'smultiplier.Wethentotaltheanswers.Seethetablebelow:Equationofcurveofrevolution:Y=x.HenceArea=r2andcircumference=2r.OrdinateNumberAreaSimpson'sMultiplierProduct101023.14412.5636.28212.5644526471TotalProduct=Spacingbetweenordinates=b=1Result=(b/3)xTotalProduct=FindingSurfaceAreas:Weproceedasforvolumesonlyusingcircumferencesinsteadofareascorrespondingtoeachoftheordinates.OrdinateNumberCircumferenceSimpson'sMultiplierProduct101026.28425.123244526471TotalProduct=Spacingbetweenordinates=b=1Result=(b/3)xTotalProduct=

Description
Sheet explaining how to find volumes of shapes of revolution, numerically in terms of Simpson's rule

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