6.2.pdf - u00a76.2 Volumes Some well-known formulas Volume...

This preview shows page 1 - 7 out of 11 pages.

§6.2. VolumesSome well-known formulasVolume=Base area×Height1
Find formulaQuestion.LetSbe a solid that lie betweenx=aandx=b. If thecross-sectional area ofSin the planePx, throughxand perpendic-ular to thex-axis, isA(x), then find the volume ofS.2
FormulaV(Si)A(x?i)ΔxVni=1A(x?i)ΔxV=limnni=1A(x?i)Δx=ZbaA(x)dx3
Disk MethodTwo forms:V=RbaA(x)dxrotating about x-axis or liney=hV=RdcA(y)dyrotating about y-axis or linex=kKey point:Find the cross-sectional areaA(x)orA(y):(1) If the cross-section is aDISK, then we find the radius of thedisk (in terms ofxory) and useA=π(radius)2.4
ExampleExample.Show that the volume of a sphere of radiusrisV=43.
5
6

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture