I9Odd   1Courier NewTimes New Roman1Courier New1Courier NewTimes New RomanTimes New Roman1Courier New1Courier New1Courier New1Courier NewXPXPXPXP{ d< p {W?[Ap#JO@JΊŕ@yϋ׃Iփ@ ???@@@@@@033333??@^ߛOw?̌???a |;@NTaTa@@?@ @@@?@@2??h!@$$$h!@???????蚖웖@a!r = a; 0.000000 <= t <= 6.283185PPP 2 2??@$$$@???????@?ْ ڒےܒݒޒ ߒL|$9(b+d)*(sqrt(a^2-(b+d)^2-x^2)/sqrt(abs(a^2-(b+d)^2-x^2)))Xy = (b+d)*(sqrt(a^2-(b+d)^2-x^2)/sqrt(abs(a^2-(b+d)^2-x^2))); 0.000000 <= x <= 5.0000002???$$$`2@???????  LT,00sqrt(a^2-b^2)bseg (0,0) to (sqrt(a^2-b^2),b)2???$$$ bp@p= ף??????? $(,048<8\T00sqrt(a^2-(b+d)^2)b+d%seg (0,0) to (sqrt(a^2-(b+d)^2),b+d)2??h!@$$$h!h!???????? $(,048D$LA|3Dпha*sqrt(arcsin((b+d)/a)-t)/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(t-arcsin((b)/a))/sqrt(abs(t-arcsin((b)/a)))r = a*sqrt(arcsin((b+d)/a)-t)/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(t-arcsin((b)/a))/sqrt(abs(t-arcsin((b)/a))); -1.570796 <= t <= 1.5707962??h!@$$$h!h!????????@DHLPTXo8vk8̦nha*sqrt(t-arcsin((b+d)/a))/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(arcsin((b)/a)-t)/sqrt(abs(t-arcsin((b)/a)))r = a*sqrt(t-arcsin((b+d)/a))/sqrt(abs(arcsin((b+d)/a)-t))*sqrt(arcsin((b)/a)-t)/sqrt(abs(t-arcsin((b)/a))); -1.570796 <= t <= 1.570796 2 2??@$$$@???????@?<@DHLPT!h''-b*(sqrt(a^2-b^2-x^2)/sqrt(abs(a^2-b^2-x^2)))Ly = b*(sqrt(a^2-b^2-x^2)/sqrt(abs(a^2-b^2-x^2))); 0.000000 <= x <= 5.0000002???$$$`2@?`2@p= ף???????\`dhlpt<ӢL(PS4Ӣsqrt(a^2-b^2)bsqrt(a^2-b^2)b+d-seg (sqrt(a^2-b^2),b) to (sqrt(a^2-b^2),b+d)2???$$$ bp@p= ף?`2@p= ף???????X\`dhlp0xsqrt(a^2-(b+d)^2)b+dsqrt(a^2-b^2)b+d3seg (sqrt(a^2-(b+d)^2),b+d) to (sqrt(a^2-b^2),b+d)2??h!@$$$h!????????x|QHTpNDZl/1*sqrt(arcsin(b/a)-t)/sqrt(abs(arcsin(b/a)-t))Nr = 1*sqrt(arcsin(b/a)-t)/sqrt(abs(arcsin(b/a)-t)); 0.000000 <= t <= 1.5707962??h!@$$$h!???????tx|–ÖĖT膤/1*sqrt(t-arcsin(b/a))/sqrt(abs(arcsin(b/a)-t))Or = 1*sqrt(t-arcsin(b/a))/sqrt(abs(arcsin(b/a)-t)); -1.570796 <= t <= 0.0000002??h!@$$$@???????70Dq 43a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))t[(x,y) = (a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a)),t); -5.000000 <= t <= 5.0000002??h!@$$$@???????ŖƖǖȖɖʖ˖XҤ¨Ԥ'ڨ4-a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))t\(x,y) = (-a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a)),t); -5.000000 <= t <= 5.000000(b+d)*(sqrt(a2??h!@$$$@??????? ݧFXH(L(MVt3a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))[(x,y) = (t,a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))); -5.000000 <= t <= 5.0000002-(b+d)^2-x^2)/sqrt(2??h!@$$$@???????̖͖ΖϖЖіҖxgt *t4-a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))\(x,y) = (t,-a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))); -5.000000 <= t <= 5.000000bs(a^2-(b+d)^2-x^2))2???$$$Gz`2@??????? e8kΪl0-asqrt(a^2-b^2)b seg (0,-a) to (sqrt(a^2-b^2),b)2???$$$??????? ӖԖՖ֖זٖؖ400obseg (0,0) to (o,b)22??h!@$$$h!?h!@???????X \`dhlpLL֭.Zsqrt(a^2-b^2)+.75*d*cos(t)*sqrt(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2)/sqrt(abs(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2))b+.75*d*sin(t)*sqrt(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2)/sqrt(abs(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2))(x,y) = (sqrt(a^2-b^2)+.75*d*cos(t)*sqrt(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2)/sqrt(abs(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2)),b+.75*d*sin(t)*sqrt(arctan((sqrt(a^2-b^2)-sqrt(a^2-(b+d)^2))/d)-t+pi/2)/sqrt(abs(arctan((sqrt(a^2-b^2???$$$`2@?????? 048<@DH|ǮQ˳T(00sqrt(a^2-b^2)0seg (0,0) to (sqrt(a^2-b^2),0)2???$$$`2@`2@??????? `dhlptx̐`δD{sqrt(a^2-b^2)bsqrt(a^2-b^2)0+seg (sqrt(a^2-b^2),b) to (sqrt(a^2-b^2),0)2??h!@$$$h!????????tιРRsqrt(a^2-b^2)+.75*d*cos(t)*sqrt(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2)/sqrt(abs(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2))b+.75*d*sin(t)*sqrt(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2)/sqrt(abs(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2))(x,y) = (sqrt(a^2-b^2)+.75*d*cos(t)*sqrt(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2)/sqrt(abs(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2)),b+.75*d*sin(t)*sqrt(arctan((-sqrt(a^2-b^2)+sqrt(a^2-(b+d)^2))/d)+t-pi/2)/sqrt(abs(arctan((-sqrt(a^xyz{Gz@?`(\?JXT@@@@@?@@@@@@@@@@@@@@@@@@@@@@   Archimedian Property of a Sphere to to chord = Pi*L^2 = pHT4r@7?i.@ldx@Times New Romanۖdzhimedian Property of a SpherehPt3P@I!~ mTL &MU?|#b?Times New RomanTܖSimilarity: ds is to dz like a is to r +B.n?pdVZ?aÒ5#/?C+2?Times New Roman ݖ2Pi r ds = 2Pi a dz dz like a is to r n(b/a)-t)); -1.57079 ƪ->_~vtZ距*,@?Times New Romanݖzi r ds = 2Pi a dz-b^2),b)(t-a))sqrt(t+a)/sqrt(abs(t+a)));zaÒZBBK?[4?Times New Roman|ޖaPVYAnbfKP3PhPPMPS>?`Y4)?}?l4? E Q?Times New Roman4ߖLPTغlۺ ?غ\ٺ ]l?=4?bIEK`ӽbzZ<Times New RomanߖrPٺKP3PhPٺٺt3P網?Y"?p#b?Ndظ@Times New Romanr^2 = a^2 - z^2N+9? ?1?D@xN"@Times New Roman\ L^2 = (a+z)^2 + r^2 KP3PhPܶ[wGiͧbMpNTimes New Roman  dS = 2Pi a dz of Surface AreadS = 2Pi a dzt3P͜oH]|L`qp2|rTimes New Roman So, the element of Surface Area dS@?@y[nRdq]G^C6QFTimes New Roman L^2 = a^2 + 2az + z^2 +a^2 - z^2S8ݹi?+LF鶟8Times New Roman< L^2 = 2a^2 + 2az z^2 +a^2 - z^2KP3PhPݹ`! bэ7UĊGTimes New RomanSo, LdL = 2a dz]LۺackgroundEPPwF f^s i`K^bэ7UTimes New RomanSo, dS = Pi LdL3PhPt3PP#K|-HdK^bTimes New Romandtds dS = Pi LdL(abs(t+a))); -5.000000 <= t <= 5.000000arcs  @NV@P~ S?؇a?Times New Romanr = a; 0.000000 <= t <= 6.283185p/^@YCc}0 T@y = (b+d)*(sqrt(a^2-(b+d)^2-x^2)/sqrt(abs(a^2-(b+d)^2-x^2)))p/^@YCc}(@P/6ahwseg (0,0) to (sqrt(a^2-b^2),b)a)p/^@YCc}H ;y?Dseg (0,0) to (sqrt(a^2-(b+d)^2),b+d)p/^@YCc}@~`I?r = a*sqrt(arcsin((b+d)/a)-t)/sqrt(abs(arcsin((b+d)/a)-t))*sp/^@YCc}0r ?@,r = a*sqrt(t-arcsin((b+d)/a))/sqrt(abs(arcsin((b+d)/a)-t))*s p/^ŕ@yϋ׃F?*+`F4Q?Dxply = b*(sqrt(a^2-b^2-x^2)/sqrt(abs(a^2-b^2-x^2))); 0.000000 <p/^ŕ@ ?HUC@?Times New Roman$seg (sqrt(a^2-b^2),b) to (sqrt(a^2-b^2),b+d)|!t3Pp/^ŕ@ ?(w?ijwdí tseg (sqrt(a^2-(b+d)^2),b+d) to (sqrt(a^2-b^2),b+d)**p/^ŕ@ ?ݖ7?t\S _dSI   r = 1*sqrt(arcsin(b/a)-t)/sqrt(abs(arcsin(b/a)-t)); -1.57079p/^ŕ@ ?ugڃ?TTTKP3PhPTTt3L r = 1*sqrt(t-arcsin(b/a))/sqrt(abs(arcsin(b/a)-t)); -1.57079p/^ŕ@ ?Q?||PɴP, (x,y) = (a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a)),p/^ŕ@ ?pO/`?TpPPpP (x,y) = (-a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a))p/^ŕ@ ?xT]]@, (x,y) = (t,a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+a)p/^ŕ@ ?.VG衴U8,{(x,y) = (t,-a*sqrt(a-t)/sqrt(abs(t-a))sqrt(t+a)/sqrt(abs(t+ap/^ŕ@ ?7wll@@,Xseg (0,-a) to (sqrt(a^2-b^2),b)wp/^ŕ@ ?mwwL₺YAKPseg (0,0) to (o,b)׺U88/p/^ŕ@ ?X*/(غߺX8(x,y) = (sqrt(a^2-b^2)+.75*d*cos(t)*sqrt(arctan((sqrt(a^2-b^ p/^ŕ@yϋ׃L2lseg (0,0) to (sqrt(a^2-b^2),0)̳Pp/^ŕ@yϋ׃ <=MlYA <0dʴ]Pseg (sqrt(a^2-b^2),b) to (sqrt(a^2-b^2),0)e5˳Pp/^ŕ@yϋ׃W;䫵(x,y) = (sqrt(a^2-b^2)+.75*d*cos(t)*sqrt(arctan((-sqrt(a^2-b p/^ŕ@yϋ׃0+