G.GMD.I WORKSHEET #7 - PATTERSON NAME: 1. Match the following terms to the diagram. Given the value ONL ;Tii:F:,.r C-. L A D B I prism with face BCFE as one of its bases. Use each 1. Edge A. Rectangle ADGH 2. Lateral Face B. HF 3. Base C, 4. Vertex AD D. Point 5. Height B E. Rectangle HDCF raises her hand and sav< rectangle BHGC?,, r.t_ rng tady in ttre ctasl ..-_ -'.ra,,t) r ;i;JJlt'l^TI;'"1'J;?"11[,'ji.:T ;::',:::,"J#::i,li:,,,iiffi ;;;; \-eS €tflvt(.E*sE B ; ;A" ;;' coeLj} tsE *?qAr-tE : Cs..ra.trZr€nJT oplbs 3. Properly name the following prisms. a) coc-.S ,oClrLN :,:, ,E-:";ilffiE: rc€- FActS. b) d) - cvBE Name: e) Name: Hio* f) Name: OBr-rQuE Pear. oZ ?ao,,tStgllr*vc) Name: P!_AX Uex*e,^"*c pcUft ftsn- h) Name: ttand how vnl,,-6 tt,^-t-- i--what is inside the shape... for examole, if .,.rrr .rr-..r^^_r r. ffi"ffi , *lllX,*aor, *1[JI$,,#":'#;;T;*:*i*":i:.1y;ilT:,;XIJ[::il#::lx,IJL.l; ::::::::::l:::ffi (,rrE PteLe ut pdper mu E,ldtttPtr Lu ffi:ffi ::.:11::+;,ffi'"*,[::,:",Tlffi il1;:T::":ffi . oy or rne sracx'-'' ruire rs srii confuseci, can you grve another Ac)uxro cb CAEES. o AetrA oF- | .p cas E - tb3t l- .rF stlrc)<- G.GMD.7 WORKSHEET #7 - PATTERSON 5. Cavalieri's principle says that these two prisms have equal volume. Explain why that is true? + sxna H€t ulrr1 * SFna cBoSS SEctlcrr.S \ AT ALL LEveuS ( rz ..*'t ) 5. !f the Volume of the cube is (4X4X4) = e+ cm2, what is the volume of the oblique prism if it;f na5 has I,een been tilted filfeq af at ou 60"?t I {hNo cH}t-r6'g rN Vor'rng.r - STFre HgtH{1 - s*rYe 8AS a - +cm = AGIA cc,ess SEcacnS Vauu*/.E-= two prisms DO NOT have the same volume because the cross sections are not the same. Renee disagrees; she says that it isn't the shape that has to be the same it is the area. Renee thinks they have the same volume. Who is right and why? -THL 7. Jenny says that the ?.,nq-Z $ Ccru?i.c;T. U U tLL -THeSl.rft{)1S f,o-A Dr ff TYL6t"sf , AaTA oF 'THL CCoSr 5g6flcrr') t\ 15 E q.,r.$gJ. I tr\(tz\ a 30 u"z ,(().j5.*] Vour, Y1i.- = water. When the glass box is tilted on its side the water shifts places. What is the relationship of the water before and after the tilting? What is the height of the water when the box is tiled upright? 8. An enclosed glass box contains 1620 in3 of a.) Vor-urr E tS = (5) (z+)(v) E l6 20 rrl 3 trr ) cL\ l{ov6-D . b) tz (rg) (^) = 16Zo,'i x = -/.:27 in. I G.GMD.7 WORKSHEET #7 - PATTERSON 9. Randy says "Cylinder volume is easy does Randy mean by this? - it is done the same way as a prism except its base is a circle." What Pa,s SflLL f,UST Besa Ar-(A x 3 r't ,l 4Yr-tNDr./L !=bt l. I V=bh W v=EgL , 10. Ryllie looks at the two cylinders below and says that the oblique cylinder has less volume because it is at an angle. The volume for the right cylinder is V = n(g)2(h) and the votumq for the obtique cylinder is V = zr(alz(sin 73'Xhl because it is at an angle. ts she correct? \ N OpE I . HE\6rH6 BaseS TUL AOL: = p.r..rA HEIc/r|-( t^rlS NoT CHAN,ED mAldN& -Tt<€ cYUr,'O@ o6Llg\t . 11. Jared wants to test out a new theory..... lnstead of having the cross area sections the same as Cavalieri suggested he wants to half the radius of one cross section and then double the height to make up for it. He believes because he divided the radius by 2 but doubleyfh{ height that the volumes should be equal. ls he correct? Explaifi )vtceT lwD€ 6ys1noF,2 Bh V= fr (q)'( s) r.-\ S.? /rrveu: ton * f,n,, DIDN'T wa?-V B€cts.rSE r I Nf n\ f*r-rc\utn ori. V= Btn6 (z)L(ro) 6o?f e,",L TI4g gEu}1\o$r,tr 5cm r,^,.= r S Srfirv]nt$ { P. ll - ll 12. A rectangular prism and a cylinder have the same height and the same volume. What is the length the side of the prism's square base? ----Z h h ,{ ,'.,.""""'t il""""".',., x t ^ , .r Lt V=r(q)'h v =x n (rO/ = *")( . 16'tT rl 161r' '+ JTI - 5cm : Scm : =xL =x =\ 2-t h of
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