ࡱ> 5@ 'bjbj22 ,XXx6666$ vvvH J J J J J J $ R n "n 66v?  68v:H H  )  n  -| H 0 ,F 6666 X n n Intersection of 2 Spheres Volumes 1. Find the volume that lies inside both spheres: x2 + y2 + z2 + 4x 2y + 4z + 5 = 0 and x2 + y2 + z2 = 4. First well complete the square and 2 spheres with the same radius of 2.  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and x2 + y2 + z2 = 4 So our total volume inside the 2 spheres is  EMBED Equation.DSMT4  Where A and B represent the 2 double-counted volumes inside each of the spheres. Now the intersection of 2 spheres is a circle and to compute the volume of a polar cap we can look at the volume of rotation of the circle like: x2 + y2 = R2 or 22 as is the case here.  So if we have 2 spheres (or circles) of equal radius intersecting all we need to know is how far from the centers is the plane of intersection. Let a be the distance to find volume A and b be the distance to find volume B. The distance between the centers of the 2 spheres (0,0,0) and (-2,1,-2) is  EMBED Equation.DSMT4 . Now we have to find the plane (point) of intersection Since the 2 spheres have the same radius, we have 2 congruent shapes. That is, a = b and A = B and the plane of intersection is the midpoint of that 3 unit segment. So  EMBED Equation.DSMT4 . Now plugging this into our formula above along with R = 2, we get: VA =  EMBED Equation.DSMT4  VA + VB =  EMBED Equation.DSMT4  and so the total volume is:  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  so all we need to know is a. #$XY]^bc      ' ( , - 1 2 e f } ~  j k o p t u { | ķjhsUmHnHu h$n:H*h$n:jh^hqUEHUj!D`!^E瞻>!+0DxڝTOA3]B$ i @H)Gqj*n Җ4!b4x"MgC M14Tgwf~7k,fh0H ;%V'5C1zutB ~doanl OM ½}@?p DDj?I_/:GAD8Πt(nt+nGqstVq/npr"#~}S"=")AZ6Zl˭CeA Gv+5 @70wR[L32d=ԿKw֮yYUQ֧uru*c/mT׺[ڎb6pvvvʣH\'n8v0#|%lƦgME_ 0^SUssW2>;0n c|z>cͤZyf$j\r.m&D(^,RMީgiw38G;g$"/Ƨӟp63hr<wy fPl/)` >oK̭oPXBښL)7KK" BJ-.j7= VBB 7R:XiPwKP#0Rwi(!՟N5u{]1g|ȻGRr}:o.~8 nDd 80  # A2#cCw[`!#cCw[  D#xڭUkA3M&ml I j%bC.I@AզA.GIR~ ^?zyI'ORDofQb418}ߛ,;1 -CI Hm!&;:95g}(1X&ʯqg>c儔Z74 Q.שq~7v5ܴ&~e@<詣 [-p(7e*%|}\(B{$Mrˏ0ɴA)&}0,' JVqIt\KTb ~rW.C=D%SAb'8)7Xt.NvϜ2%cu?ó}l?t٨i}[.0LBnbZlBb[1+&MŢۭ[* QU:aY!~]%y,]NGSُ%EC% 9.ݳ.H&jChi0RRm*5Vȋ6ZVxJ;x.-7[+zZ*vlCH"ٲ/Kbc F3q\7L*W)Q'sw2xm{oF syu8 DHoi Z8LbhK,ZyuKim0;-qOch(lZc" քP2\zcH*Qq](a;1%[.Ɋ2CǘHbf;Hy谮'ySU>c׼̙+tq{%쟪%Aeۡ{Y -SYDdfH  C $A disk1RSY_Q2퇡Nɥ/Y0 F'Y_Q2퇡NɥJFIFC    $.' ",#(7),01444'9=82<.342C  2!!22222222222222222222222222222222222222222222222222 @" }!1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz w!1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ?( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (+E۴eU 1ezՊ⧅Ce}!QJ3q((((((((((((((((((((((((((((((((((((]WƆA'NT'%$θX(͕(qh((((((((((((((((((((((((((((((((((($ 9t !"#$%&'()*+,-./103254678su:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrvxyz{|}~Root Entry< F #Data eWordDocument;,ObjectPool>  _1195147316F  Ole CompObjiObjInfo  !"#$'*+,-.14567:=>?@ABCDEFILMNORUVWXYZ]`abcdehklmnopqrstux{|}~ FMathType 4.0 Equation MathType EFEquation.DSMT49qJ@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  x 2 ++4Equation Native f_1195147412, F  Ole CompObj ix++ 4++y 2 "-2y++ 1++z 2 ++4z++ 4=="-5++ 4++ 1++ 4 FMathType 4.0 Equation MathType EFEquation.DSMT49qy@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  x++4() 2 ++y"-1() 2 ++z++2() ObjInfo Equation Native _1195147547F  Ole 2 ==4 FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_CompObjiObjInfoEquation Native _1195156266 F  A    43 p2() 3 ++  43 p2() 3 "-A"-B== 64p3"-A"-B FMathType 4.0 Equation MathType EFEquation.DSMT49qOle %CompObj&iObjInfo(Equation Native )F*@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A   2 2 ++1 2 ++2 2 ==3_1195156985F  Ole /CompObj0iObjInfo2 FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  a==1  12  or   32Equation Native 32_1195157199"F  Ole 8CompObj 9i FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  ==p  2ObjInfo!;Equation Native <_1195157253'$F  Ole G"2 3 3 "-2 2   32 ()++    32 () 3 3 []==p  163 "-6++  98 []==p  98 "-  23 []== 11p24CompObj#%HiObjInfo&JEquation Native K<_1195157430)F   FMathType 4.0 Equation MathType EFEquation.DSMT49q @6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  2" 11p24== 11p12Ole PCompObj(*QiObjInfo+SEquation Native T FMathType 4.0 Equation MathType EFEquation.DSMT49qh@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A   64p3"  44 "- 11p12==% 245p12 FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G<DSMT4WinAllBasicCodePages_11951555771.F  Ole [CompObj-/\iObjInfo0^Equation Native __119515578463F  Ole fCompObj24giTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  dV==pr 2 dx==py 2 dx==pR 2 "-x 2 ()dx FMathType 4.0 Equation MathType EFEquation.DSMT49q@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  V==qpR 2 "-x 2 ()dx x==ax==R +" =ObjInfo5iEquation Native j_11951558508F  Ole v=pR 2 x"-  x 3 3 () aR ==pR 3 "-  R 3 3 ()"-R 2 a"-  a 3 3 ()[] FMathType 4.0 Equation MathTyCompObj79wiObjInfo:yEquation Native z1Tablewpe EFEquation.DSMT49qc@6M6G<DSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!O!(u!APAE%B_AC_AE*_HA@AHA*_D_E_E_A  ==p  2R 3 3 "-R 2 a++  a 3 3 []\ozGr}Vq]p>%ů-y_n ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (8]i?wEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQESaO ( ( ( ( ( ( ( ( ( ( ( ( ( ( (8_>)xK_۽wU=/'U\TѪ@f4QEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEs3Y5H&yې":z+':'^ RH[J]A#ެ_o}E[#-qg*3q3\ĝ. NSpgsB2mGP1e靔<~m Zgqs܁̱`0y =w?qųN3Հv i*?CXW 3|wI$p(26eRcsaƘ3Oխ0 1ղt@Ey[%aj:LĜnHOvz~y}K)~EPEPEPEPEPEPEPEPEPEPEPEPEPMQ@Q@Q@Q@Q@Q@c=h(((((j:M] qRz:{{ #|}%_X\!KOx!zqk~o7[FN{rGR}5{Ohr]D_) dU'֛ku\kQйv"UD P'uvc/l>m'&iB eQEQEQE;xHIlI1Ыϼs|q7neyA=v2GEPEPEPK>R6p]@H&9Epڿ]&quiib'_^ExIlI&XQtO8`rKC~zVŨ5M1.෱eW+!t<w.2W yP0m{#+$W^4w$A#sfHP)Þ*KImChRGRd9$}^|B jEl. >Xdcmf ڊ((((*ZZ|Q-Gqq^(Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Vneu[s9$@Uk>>iuѼ%b5W%]YqDZFH|G\Oa-noP;|GGqnbz]6(*XOɠGMvw뺞!F{ϦkUX*S(((((=##` X6+׵zyur/=_I((((/ [G?+c?;gO#NA5[Kଋ:&G͍ۗ 㞕@SLBc?vl/OCZVvuʀ^&xrF{r ՛>T{Khm߬ra.o N4eHWRrݱ< T5zGǶ>!;YCz I(x$vQEQE-dh:$Yae1j=ڼnbv =*΀i$U[%>Dn:+)%AG:*i:|Ӥ6)y$cnQId@ wɅrsq=*pCA<(w־n4 { Bdz*Oַ5j w *ї>͑V=+ϾO|<\RUNxTJ*( ( ( ( ( ( ( ( ( ( ( (Kž/:)LmQ EV?03H^!"IwrvZXA̷J<#}.= -u#?L^eu{Cr?x? ` ( ( ( ( ( ( (#oUBov^KuuQ@! @o⿇^k&H 8n6i.T0ʲml#ux}}N?^2W#oCt+_ӮNQTy$\cÔ=IX2R# t;A[2&|IeWŮs\0ndt~#>ÒA/-[uYT(1Vyuő/M.WI Ybq(V7ս i&O V98+8<+4(mdVwd߯NC^|:Фra}wGj +摧Qj0mPH!'E(בT~GMgnsm w}˵wZƟY儼}W Iw+kdcX2֧vM~SGV=Ug$$Ҵa},py$F{_W/⣴_ͳנ8Gxλ(((()T"hv:d p*(((3 !U٩DiWPsaO^:s^uΙ*hzsrA\@gW|JО_d4KpVqҤc c(Ww1 6D?Ĭ0G+~h {d?>=8n0{Z TݣYH5IG? tKz4R$,0ʲ=A}ai=w0ȹY >"h|x1$QPP0 [__aa#@`%<3wcYt]KӬXOE}OzEQEQEQEQEQEQEQEQEQEQUఴU/$xU$/|-Mm8H|H~ o%S'wJR bw..'DKoO9Ш((cƌQFI=T~n/yw&#99 5K-P#V֗QI2zG$מ=mxdl5`2!b1˴5.Ck^''+*oj9Yb` Њ(8u~,޷[G}c!!6u/g2N3^WaH`+l5{ac—2qMm+̬Q>xZ naVݏ@y@99c ᨭ5`6~p@8U]ׂA'tR=FVc،0nEQEQEQEQEQEQEQEQEQEQEQE=xUiHP=3\]Nt?2mu03KSr:PRN,td +,TpȮuZ։%5U((((((((((N+ 떣]Wך|l,] MZ[61^@SNr0;(((((+hl"iuBd@I0rGQ}qʼQSou7rN6}N#S mp}v^t"m!X˅b=I>4W2EQ ;{,]er>x?zKH s#luoU\ q7aX^-gZgzy~[+kQǧ|A;nhN،zoQϷcx?WǖFyfAzkZ=ޛv3f7Q{u? }L˥n8S>I{ 6s^^K[DqZ;XjJel0{a[nO֨_zK&͕z1:*(((QEQEQEQEQEQEQEQE?=Nهnl`X`c>].8U=" [y^EYCm)9 >s.O-TemAԣ`FT8I(((((((((((3۟Clq «m-7ο}O#z}QERsޖ ( ( lnqh0Y[)ܮ T諃_ߍvG/@Q@Q@ymB~$fWHZLs \&72T:) 99q|M_tТI2v}@Y#_n`hѝrb=i}Zk}|VhkFjxKnVA꺅F'?м[s5;K*b ?s23ҽ FDFު Tj(((((((((((7DҷLeKV-=)n9jm`%#XE誣[V_ $f; {E%Xx[qڻ(((((((((((Q@a+{/ ޜXO2@m6@ ܠֽ6 ( ( ( ( wE`nˋŏ{φe[Z 0#ր=((7]oN Ev:]zfeǏ.qU[7t.$fQb7Gױ*Is 3dm~n=¹隽37_0gLT5+u<9tL]e^5xfS(H${^x+޹^QPMov$oR7r9%uZ|K|i*'-@ /SPmviou| Fs>Lw@yb[wDHHG7x$!$_+l ? ]hy4kl؜`Z5)5:[ݼ’k>j*h=)KCSHfc( ( ( ( ( ( ( ( ( ( (-y%.@1N M_-wϣ PWHn/on&RCyq@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@o3|5U~/Ra-c׏ C((((IRKp@ ,2x́2xp#zaڀ;( (<)0x{j9>7kkʹH!v]6?VmzM|+%̄3ww!#7]p? 1%zPoQ]J N=zQ$e\`5g;~kue鶳d2lPh,0:K>\Zm 1Wי|9YlbPkn#EET>@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@I^qyG_Z >4.ݍQEwrQEQEQEQEQE1]_;XEQEG#?iW#Ʈ~/+~ 5Nqk3ϻTaҎ{P$qLpOq #13AbŒG$ǀH+դH{%vH z rGxx)$[u3>/3oNsss]> 9=k⏘|{HA$Ry?}*Q1DG"#+@~lc30=^^s#y?$ ``؟?-z5-G[_̺\cOxzEp@NЯc1Xkv3P=7@>":D#[FT cF11Z'?ei-AFA-nEPEPEPEPEPEFdT$ SOEsrxQH. P$~bj,7 皕5M>B/U$΀.&uhľ'CN7vPr xc3So<9f F ,sEPEPEPEPEPEPEPEPEPEPEPEPnQ>GidJ'=kǑ]dC+у1@EQEQEQEW![OLï]BhϚe>1ݟqo;( ֥ht-BTb1BFx m>9uOU:ɉkC}|3(kEX?W_@^$/$vS:RU< }:e襧xق$˞Grj_x mvK@)V۟ J@0SVϋ!%bV=1J{{q[q)0Zڴm,HKϱiSR0i&TI%lJy rms[P:C.u',F1w\c h<|/x)˷u|,!Qs?G]ï¯ , ʜ3s5_Zh6K˃j $IU0Ooc|!s[.?SN?$u]b YbEӛMAknOGoz*(ΓkCn5lsqԀGGV&&/#8I]?P!{|Ȳ>~4OEcYۯ98z o4 -#(qaۀZlqԓ=~Q^EyѾ$'tO1Hڜ4<{uI0p" (ϤuќK"@ AߧZtљOssvz=I}Eonl`J>OB.϶@<37}kh?[YHfIՇ/`dǶq^Ey&^0\ ('D<~s{t|vqv;#^ykШ??5/}`>0T##;?__ul F^PTZj(_ g_L8P*]V+%bW@||,LY{} {*QOs98Oo 3ČGBTP|C>t73b5hA"Eo: SP鐬$H&y1 A -YZCZ+XT=qZ71sNAuybTɠexDSa cWX¹#nps?J|!>r;>Ŏe;"hҀW_pcx$(KMe8\h' :qϩ֞vm;hГ p#UK+$l G֜8K *c@>/4.rڀ^:5J `bPg+65_I&k^U:ݨ/kZe͊'gA 3sPWaG؟B%νF~|A5-@5pʸđlr3_|C1|P(+¡kj]S+9H'#oƹ^,?TӘ (N  o{OF㳎kO6WWVlgNzmfwco(((4o^T&pO0{[$sz]G ˣk1|Q_|1=PpNq((7O~f_}z|ju{?ԏƀ={튷 c^9y>7?OQ\P 6S1:lygnҀ:( ( ( ( % xx[S/̹5w|SᶴI KpnOP[\%ݤ7cW^{ҧ(((((((((((-]Z|,TGF(Cc;,W?qC|-tlU6.F7ihn(((jizu x; {מ[x?n>&GG"#fHOTW9zr ^ ӯbn,ۼ~SS.%-"(㝠N``aאr=C@Q@p'n4,RX1RO#+=|,")h\R'cSEQE`x$Sr>Sbᾈ<&Qˁn>,^@gXjEof |lwe@ h_øԘqc55Zͨw-OL$Mz jZvIYo4>K70O@?:XL,w6nQ8'vckBΣ$7W-MFE| |GK IKMR2ۗ2ȸ 7<@}ƵZN ᘜUN:^YC>'{)x8Iۄ%99wޗkob'!<6ր5(cF :.gp泂G7<@U(h[6;/T2xwD(GZP)H|;9أj3 A΍N5EQEQEQEQEKUMOHǗuza|4?Slɏ]mpɰF':I_ln ( ( ( ( ( ( ( ( ( ( (8cn }|[ ~g^ǿhxϮlQ@Q@Q@?ȥ~+;mND[sZ:4:}7WX]=pU=q]G?9h((I9`N((((((Y[E u+h*n`br{]p;MPhzw9oʫ AzPEQEQEQEQEQEQEQEQEQEQE|I~k?O^߭\CnK<%[߈!o) ֧7 ]OQEQEQEQEW<%]| {נWa,ҟϩg(i-e9ҷxRձ&Az8T_y=jt *@ uQEyb=.nl{FI?'4_V88?9q|Wq;|11-l7tܨH@W! ksLGވYҫYf|1 /mV2cߊhz~qw ,F^sڼ}3jR#,iL̷2E?{V{>M&&]R+^pLf gߕu}Ny/ldF~R@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@+ }WL/ u*s? iNH;s΢[DnNע6};Js~ z-Q@Q@Q@Q@Q@Q@RZ( ( ( (9|zinOz<A{.%xn'wӧYM' sZ襠((((I-2qҸ\Z5ṷ 72e @Q@r~klf$"NwֺZ.X!n!x5r${C\ ]y{ߴ;ٔWS(=C2s:סEPbkēu[ ~jvf^shOJ`OS5Ǐ~!^HISGn3(j%,(YD֧ob tPͻqp6|?ޗDZtP*vsVAu[V4xrx<#i9]2ȹZB0A ,qD`**aOwz4wp7 ŷ¶+|6?qxaqFHF} ( ( ( ( ( ( ( ( ( (0|k"'}?.s~{?l?Ծ4'pp.y?ɪ>l/O(((((d`yt4ɘ2UI8|.ƍ<Hg"F%?Ҁ;*( (:Ҕa-G|"K5LiegǶ"I!ֽ* c2b'//OvHՔ9v#d\\xSQծښH{¡Ͼz ^WJԤ'Cx Eh+OcE+y!7I]OZPTvdDP9;NZ6Gghc3`Z˸,l缹GH碨'!w>}Ky5 P Hw?pgPOIG_JZO:C#'heEoEQEQEQEQEQEQEQEQEQEQEQEQEq<=qhQϧVӦvRלwZ^)r8)<;`N20qoW>2xw]1«nU9(kjx a8뎱U 1M(((( Ox#^#ӮɪÕesϼ>t 9.cY!6D=X`Tzvo"bprI>r((2˦i:3KĪצ_L}[ᦵo5{pG5mxOXzVZ6{dy6tY1ۇ@U]ȼmVY:~-m@%^hZ%qp3Ƽ1Kr3/OninX(dFgὣO_H~ 7dKH"W+w^?\Zvݣucē8dn+֟FlG Pay:Y<9~2q"5aZvmiYZR(T*}I=؞Ipkb28oæ zEE,I4MC@X_[jv0L[L:0Un>J%W*m)'8ջ|iwo}iլ592P( ( ( ( ( ( ( (3{I3$c,Fp2G?.eoy nG"ּaWLo.22nܷ4xvCGT2meUX?`k]2-oAP0VP#'nyRY21Yujpb CMw{]wT2x•9 @s@'q9/c^ʙI N8l;AEt-?3H j( ( ( ( ( ( ("CoJ )ѾQ%wn7#/p1 FMQ-wQEQEQEQEs?N> 8ZhCB"k(J/W`+|ggsf{ kl=P( ( >%_irQiw-%hᬣ%T;*NW8fۀ@gMn12pzx)9a][R"Ez0=_ BP_3*OluNQP..m'* @((/ xOMךi۸6ˎq0#[_Ew[ $rZT+swQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEx׶WS~@|x1Ccs@qψn$ 1@I1žƽNAwxNplpU5RJu2k|9eQ$1c2;#`@Xz4[4|Cm]{_2bkr ( ( ( ( ( O&O<|)чWQ%wGph\DEQEQEQE|]uOzn$@JV]"X`c*wȽzWo gA(J(Cľ>t{8{#m s4[Zsu2Cc/#+5j&F𥬍 *K1G$Aҥu+k7åx sp=M,$H`N9xd}wf*QS8OP{;)'KIH(6l(j|>#^'C?t62'yX[kWA*nRэ#^s(ּh֢kgȉ+(spJ>n:zU#KaR I^i2)m,|/tZj {Ywz$&0εψE]G'iHAscA_O rCvϔt: ]bU QEg[_ jY!0|.T1o1E#8ύq>-UzEe͎\yڪ9iTA@ VtIŋg[eU@6x4XO Ipx׋־$xN\Nv{ݰs( 8^볨x'BfR;3/E]ntOm3,i#*Nw&TΫZs\;^K20#r?A]ݥpG<XPh I68lJ{Fs:gl_ uӃĖ:y Y؇$#>dV.$f*<*II[zX% ܤ`9QȠoI,k[mYC;n$׌ڼoSzn\m;ِ ?PAIҾYZHWk. I#^셗Q LW``9uSCMѬ# pkxvttɂ-lOc}^[`g2uW+6 m>N oV`5!7AР$f]AIj㷺kekcxXP GQg7>(5yEhm\;ϭC}/ xvD[Ulnlcv1[P/w:5LkiAlɑ\e"((({Kzg5|\eռH6] PEPEPEPEPEPEf ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( lT1!51!N>zyoOj^ZEeP@EPEPEPEPEPEPEPEPEPEPEPEPEPEPEPEPEPEPM}PEPEPEPEPEPEPEPEPEPEPEPEPEPEPEPEP^]0m𶴘je1]kk~ E,Z'D۷}0HTQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQEQETnC G˾=IsS@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@Q@FqKEQEQEQEGDd 0  # A2mEm̚6e`!mEm̚6H@ hxtexڝSkSAf7/m~hւJDZžJoI`SMIbԇ 66-ZX)x7/rOCH$]!Zn0EbGjf4ebx'˚%~3yFZoZmL`7]^-Կ&{-xLT*jγlON0Oʬ{C0>*ʈJ~L mG[-Jwf{Lcn@/On'G~.{YX^)WoS?>5]\X[St|~iŏ&.{NrPwse63KseNh/-WZV۰6ܡiADa^++hIFi0Nj(=;Ie9,IL| kw`P*@yV=݁!>}pOr^;K!*_\;VSTdZWxϳW&}H_:Dd d0  # A2c>3W0@ Zwsk`!kc>3W0@ Zw ( >~ 9xڵWMhG~3+[VІ4:Ul\*GC8L(mqDT;IC\_ S/m#M[)!8 p'VZF^V3o{p.>&Xrِ%[: ? ­(vip\GM;Ϊt6UgH3ja`\T¦Q?θԊSнr󡦵Qڠnw%@?\<7*k̶/x3 ؄WtaȦNl֎M6#!*VTXIg~H,]y;o|}),] r.jpobf_~'t_M ]g B76u 2 GScG/s X#.oog/q~*5tx6ƯzQ]za¸Os0cGzb}}WtQx6-NqI̿!ޗbb#5qfz$WZt/Tfo==0L9VlíE=ҡ{E:\N5 ʍISRZfs`]4[k{EX#hzbjlV֓^,[mVɰǚnԣlo˸po3GcG3uucu\/O۬OctT&r|x0oؙ c驱s)k4*Xf! ɯ'7lO_{R)iO%O@)Y(-Eɯ n!Y=QZ04}Dd Cpv \ xޠKҥ"3`@%"%xp|ꨶ_KS-?1jU 3+a|r.wA:г}e` Og?{x@*ŪCUaVC?:bc`5jЊsĮa~K&4\L@;;/M9^wfT-Dd 0  # A2s8a=Cp`!}s8a=C| ``PKxڥSAkQ&vM+l r6 `4.m iB"Ez؃ox.e8ݴF>~;3{3Tv(|pSB>c%k*χʿfd7DFU9-xX֝m셺ArFԸG $ǀށqP!KsɎSҳ!9D=T"9w'%=6ExBUԞԫ V6hVOBiɲzlR T[)Ǖ Z][SלDa^>@٬8M"J2rMf`* _?;q7Y=~p,4͹Wb墟sn_ /Q1KS<BqaA e l'q,3>CIx/574k|O%]O[s,,0bvjK8Y߂pHJ6&eҘDd < 40   # A 2`_ĤjXs`!`_ĤjX` HbpxڥTkA~3mpZ6)TLVL*X[K=hHФh@b"KœB{I)҃"=xPff'X̷߼y߼7? &cf)er:SK!1<@f |pk凩le9]-ܽ0H.& !7)OWW^CqoMMCiq(N.ˮ"]n[Sܶ&9uZҺ[2gDFt`}kXȮ`֌Z_2fwbħƫugvRThx.?vG٦{*Dݨe%NMxVoVX;^\g2ù 2wMA}W zPYz#ٽNg FOr$8) H9IgC0 M"Hd&2)IO0b HQLo(Y,%3dq^'EZ؀14ldJ6&z[h=l7`&+PSQ j>i&aj{G1--~-w\V{uz͝`77}9|H2Z^|-jf'/P0_d#Jo)$T,b|"W$J%%8B/i&FxMSUߤx:v7_{/_2V2:)??ަxu$ _#ɓ~#|}`z"qx#1O>5LA)P63cg}ş;ktaPBZ^or{DOw36861 B\@ssfA[<[,LޘVGl& `v ¹tn7&@8ihfvMao׊Z+3+cM O4]%s-chiVR-圥ńq& EJZE[EQQX3IW@<%wsy.zu̦3)s 'bwl#ǜ9w&ADd 8 l0   # A 2ե Pf`!ե PfxڭUOA~ofJF#1-P1z@B&EI)`L]qM(%"&C ^7 Io^=y6& ( N yf8 .YY 0g/ME_.!BjdoSxK˄ ki5Ic sYɑ a- Ɲ5 |@n,vĝ HuDF%T rC r9p1!fJSu 4L"M痐b 8ě(ӯ4@-QեΙ{B!҃R*키~A^gōse?gSummaryInformation(=DocumentSummaryInformation8DCompObjjOh+'0  , H T `lt|$Intersection of 2 Spheres Volumesnte Sam Malonenam am Normalo Sam Malonen2m Microsoft Word 10.0@ @@Lc@4՜.+,0 hp   Home Teami A $Intersection of 2 Spheres Volumes Title  FMicrosoft Word Document MSWordDocWord.Document.89qD@D NormalCJ_HaJmH nHsH tHDA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No Listw'wz'$%{78*+"i+M$%(00000p0000000p0000p0p00000000000@000 M900 q '  ' & e}1IKXpr'::::::::469QSz:::8@(  \  3 "` B S  ?'d ]H&K t(fh"syM(33333333$6,L(( Sam MaloneO:^`o(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.O         Bze7*$n:"LqU]]@`7e+tnCuSds]QM@@@'P@UnknownGz Times New Roman5Symbol3& z Arial;SimSun[SO"h  94}24 3QH)?#Intersection of 2 Spheres  Volumes Sam Malone Sam Malone