已知圆台的上，下底面半径分别是2、6，侧面面积等于两底面面积和。求圆台的母线长！
\u5df2\u77e5\u5706\u53f0\u7684\u4e0a\u4e0b\u5e95\u9762\u534a\u5f84\u5206\u522b\u662f2\u548c5,\u4e14\u4fa7\u9762\u9762\u79ef\u7b49\u4e8e\u4e24\u5e95\u9762\u9762\u79ef\u4e4b\u548c,\u6c42\u8be5\u5706\u53f0\u7684\u6bcd\u7ebf\u957f\u2026\u5982\u56feABDC\u662f\u5706\u53f0\u4fa7\u9762\u5c55\u5f00\u56fe\u3002\u5f27AB\uff1d10\u03c0.\u5f27CD\uff1d4\u03c0.
\u4ece\u800c\u53ef\u8bbeOD\uff1d2x. DB\uff1d3x,
S\uff08ABDC\uff09\uff1d5x\u00d710\u03c0/2-2x\u00d74\u03c0/2\uff1d\u4e24\u5e95\u9762\u9762\u79ef\u4e4b\u548c\uff1d25\u03c0+4\u03c0
\u89e3\u5f97\uff1ax\uff1d29/21. \u6bcd\u7ebf\u957f\uff1dDB\uff1d3x\uff1d29/7\uff08\u957f\u5ea6\u5355\u4f4d\uff09
.
\u5706\u53f0\u7684\u4e0a\u4e0b\u5e95\u9762\u534a\u5f84\u5206\u522b\u662fr\uff0cR,\u5706\u53f0\u7684\u6bcd\u7ebf\u957fL,
\u5706\u53f0\u7684\u4fa7\u9762\u5c55\u5f00\u56fe\u662f\u6247\u5f62,\u5927\u5f27\u957f\u4e3a2\u03c0R\uff0c\u5c0f\u5f27\u957f\u4e3a2\u03c0r,\u8bbe\u5c0f\u6247\u5f62\u7684\u534a\u5f84\u4e3aN,
\u5219\uff1aR/r=(L+N)/N ;
(R-r)/r=(L+N-N)/N;
(R-r)/r=L/N;
N=r*L/(R-r)
\u5706\u53f0\u7684\u4fa7\u9762\u79ef\uff1a
=1/2*2\u03c0R*(L+N)-1/2*2\u03c0r*N
=\u03c0RL+\u03c0RN-\u03c0r*N
=\u03c0RL+\u03c0(R-r)*r*L/(R-r)
=\u03c0RL+\u03c0rL
\u4fa7\u9762\u9762\u79ef\u7b49\u4e8e\u4e24\u5e95\u9762\u79ef\u4e4b\u548c:
\u03c0RL+\u03c0rL=\u03c0R²+\u03c0r²
\u6240\u4ee5,\u5706\u53f0\u7684\u6bcd\u7ebf\u957fL=(R²+r²)/(R+r)
解得:l=5
答:圆台的母线长为5
绛旓細鍦嗗彴鐨勪笅搴曢潰闈㈢Н涓 锛屾墍浠ュ渾鍙扮殑搴曢潰闈㈢Н涓 鍙堝渾鍙扮殑渚ч潰绉 锛屼簬鏄 锛屽嵆 涓烘墍姹傦紟6鍒嗭紙2锛夌敱锛 1锛夊彲姹傚緱锛屽渾鍙扮殑楂樹负 锛8鍒嗏埓 锛 锛 12鍒
绛旓細鍦嗗彴鐨勪笂涓嬪簳闈㈠崐寰勫垎鍒槸r锛孯,鍦嗗彴鐨勬瘝绾块暱L,鍦嗗彴鐨勪晶闈㈠睍寮鍥炬槸鎵囧舰,澶у姬闀夸负2蟺R锛屽皬寮ч暱涓2蟺r,璁惧皬鎵囧舰鐨勫崐寰勪负N,鍒欙細R/r=(L+N)/N ;(R-r)/r=(L+N-N)/N;(R-r)/r=L/N;N=r*L/(R-r) 鍦嗗彴鐨勪晶闈㈢Н锛 =1/2*2蟺R*(L+N)-1/2*2蟺r*N=蟺RL+蟺RN-蟺r*N=蟺RL+...
绛旓細渚ч潰S=蟺锛坮+R)*l (R涓轰笂搴曞崐寰锛宺涓轰笅搴曞崐寰勶紝l涓烘瘝绾匡級浣撶НV=蟺*h*(R^2+r^2+R*r)/3 (h涓洪珮)S=8蟺l=4蟺+36蟺 寰條=5 鏋勯犵洿瑙掍笁瑙掑舰锛屾枩杈逛负l=5锛屼竴鐩磋杈逛负r-R=6-2=4锛屽彟涓鐩磋杈筯=3 V=蟺*3*锛4+36+12锛/3=52蟺 ...
绛旓細鍦嗗彴鐨姣嶇嚎闀縇=(R²+r²)/(R+r)鍒╃敤渚ч潰绉叕寮 杩囩▼濡備笅锛氬渾鍙颁晶闈㈢Н鍏紡鎺ㄥ锛
绛旓細鍥犱负鍦嗗彴鐨勪笂涓嬪簳闈㈠崐寰勫垎鍒负r,R,鎵浠ヤ笂涓嬩袱涓簳闈㈢殑鍛ㄩ暱鍒嗗埆涓2蟺r,2蟺R,鍗"姊舰"鐨"涓婁笅搴曡竟"闀,鎵浠ヤ笂涓嬩袱涓簳闈㈢殑闈㈢Н鐨勫拰涓(R^2+r^2)蟺鍙堝洜涓轰晶闈㈤潰绉瓑浜庝袱搴曢潰绉箣鍜,璁惧渾鍙扮殑姣嶇嚎闀夸负l,鍒欐湁(2蟺r+2蟺R)*l/2=(R^2+r^2)蟺寰條=(R^2+r^2)/(R+r)
绛旓細涓 +S 涓 =5r 2 蟺鍙堝渾鍙扮殑渚ч潰绉疭 渚 =蟺锛坮+2r锛塴=3蟺rl浜庢槸5r 2 蟺=3蟺rl鍗砽= 5 3 r 锛屽渾鍙扮殑楂樹负h= l 2 -( r 涓 - r 涓 ) 2 = 4 3 r 锛屾晠绛旀涓猴細 4 3 r 锛
绛旓細瑙:鈭迪(R+r)l=蟺R²+蟺r²鍗诚(6+2)l=蟺6²+蟺2²瑙ｅ緱:l=5 绛:鍦嗗彴鐨姣嶇嚎闀夸负5
绛旓細鍦嗗彴鐨勪笂闈鍛ㄩ暱涓2蟺r锛屼笅闈鍛ㄩ暱涓2蟺R锛岃鍦嗗彴姣嶇嚎闀緼锛屽ぇ鍦嗛敟浣撹鍒囨帀鐨勫皬鍦嗛敟姣嶇嚎闀夸负B锛屽垯澶у渾閿ユ瘝绾块暱锛圓+B锛夎繃澶у渾閿ラ《鐐逛綔鍦嗛敟鐨勯珮绾匡紝楂樼嚎杩囧渾鍙颁袱涓潰鐨勫渾蹇冿紝鏈塀/锛圓+B锛=r/R 鈶 涓搴曢潰闈㈢Н鍜屼负锛毾(r*r+R*R)澶у渾閿ヤ晶闈㈤潰绉細蟺R*锛圓+B锛夊皬鍦嗛敟渚ч潰闈㈢Н锛毾r*B,鍦嗗彴渚...
绛旓細鍦嗗彴鐨姣嶇嚎闀 l=锛圧²+r²锛/(R²-r²)
绛旓細瑙ｏ細璁惧渾鍙扮殑姣嶇嚎闀夸负l锛屽垯鍦嗗彴鐨勪笂搴曢潰闈㈢Н涓篠涓=蟺•R2=R^2蟺锛屽渾鍙扮殑涓嬪簳闈闈㈢Н涓篠涓=蟺•r2=r^2蟺锛屾墍浠ュ渾鍙扮殑涓ゅ簳闈㈤潰绉负S=S涓+S涓=(r^2+R^2)蟺 鍙堝渾鍙扮殑渚ч潰绉疭渚=蟺锛坮+R锛塴锛屼簬鏄锛坮+R锛塴=(r^2+R^2)蟺锛屽嵆 l=(r^2+R^2)/锛坮+R锛
