the volume of a geometric solid learning demand一个几何实体的学习需求量.ppt

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1、TheVolumeofaGeometricSolidByTyrissaSchroederPages:529-537VolumeofRectangularandCubesPrismsVolume-isthenumberofcubicunitsrequiredtofilla3-demenisionalfigure.RectangularSolid-isasolidinwhichallsixfacesarerectangles.Cube-asolidwhenallsixfacesaresquares.HHWLV=lwh,Length(widt

2、h)(height)V=7(4)(14)=392ftcubed555V=S^3V=5^3V=5(5)(5)=125inchescubedMoreGeometricSolidsCylinder-isasolidinwhichthebasesarethecirclesandareperpendiculartotheheight.Sphere-isathreedimensionalfiguremadeupofallpointsagivendistancefromthecenter.8in4inV=pie(r^2)(height)V=3.14(

3、2^2)(8)=100.48in6cm.V=4/3(pie)(r^3)V=4/3(3.14)(6^3)=150.72cmCompositeSolidsTofindthevolumeofasolidwithamissingcentersuchasacubewithacylinderdeletedfromthecenter,youwillfindthevolumeofthecubethensubtractthevolumeofthecube.Example:5m20m20m20mV=S^3–Pie(r^2)(20)V=20^3–3.14(5

4、^2)(20)=V=8,000m–1,570m=6,430m^3WordProblemAdeliverytruckis3.5meterlongand2.5meterwideand2meterhigh.(notincludingthecab)Hasalargeboxthatis1.5meterslong,1.4meterswideand1.1meterstall.WhatistheVolumeofthespaceremaininginthetruck?Solution:FindtheVolumeofthetruckthenfindthev

5、olumeoftheboxandsubtract.TruckVolume=lwh,3.5(2.5)(2)=17.5BoxVolume=lwh,1.5(1.4)(1.1)=2.3117.5–2.31=15.19meters^3MorePracticeonGeometricSolidsRectangularSolid-Cube-10ft5ft8ftV=lwhV=10(8)(5)=140ft^327cm27cm27cmV=S^3V=27^3,27(27)(27)=729cm^3CylinderandSphereCylinder-Whatist

6、hevolumedifference?YellowTube=6intall,radiusof1in.GreenTube=8.5intall,radiusof3in.Volume=Pie(r^2)(h)V=3.14(1.5)^2(6)=42.39in^2V=3.14(3)^2(8)=226.08in^2V=226.08-42.39in=183.69V=184in^3Sphere-V=4/3(pie)(r^3)=V=4/3(3.14)(2^3)=33.49in^32inFormulasRectangularSolidV=lwhV=7(4)(

7、14)=392ft^3CubeV=S^3V=5(5)(5)=125in^3CylinderV=Pie(radius^2)(h)V=3.14(4^2)(10)=502.4ft^2SphereV=4/3(pie)(radius^3)V=4/3(3.14)(3^3)=113mm^3CompositeSolidsV=S^3–pie(radius^2)(h)V=17^3–3.14(3^2)(15)=67.4inches^3THEENDThankyou!!