求圆台的母线长
\u6c42\u5706\u53f0\u6bcd\u7ebf\u957f\u56fe\u5f62\u53ca\u89e3\u7b54\uff1a
http://hi.baidu.com/jswyc/blog/item/2f07d8025b4cfc703812bb05.html
\u89e3\uff1a
\u5982\u56fe\uff0c\u662f\u5706\u53f0\u622a\u9762\u56fe\uff0cAD\u3001BC\u662f\u4e0a\u4e0b\u5e95\u534a\u5f84\uff0cAB\u662f\u9ad8\uff0cCD\u662f\u6bcd\u7ebf
\u8fc7D\u4f5cDE\u22a5BC
\u56e0\u4e3aAB\uff1d30(cm)\uff0cAD\uff1d5.5(cm)\uff0cBC\uff1d20(cm)
\u6240\u4ee5EC\uff1d20\uff0d5.5\uff1d14.5(cm)
\u6839\u636e\u52fe\u80a1\u5b9a\u7406\u53ef\u5f97DC\u224833.32(cm)
\u8bbe\u5c0f\u6247\u5f62\u534a\u5f84\u4e3aR\uff0c\u5219\u5927\u6247\u5f62\u534a\u5f84\u4e3aR\uff0b33.32
\u8bbe\u5706\u5fc3\u89d2\u5ea6\u6570\u4e3aN\uff0c\u5219\u6709\uff1a
11\u03c0\uff1dN\u03c0R/180
40\u03c0\uff1dN\u03c0(R\uff0b33.32)/180
\u89e3\u5f97\uff1a
R\u224812.64(cm)\uff0cN\u2248156.65\u00b0\uff0cR\uff0b33.32\u224845.96(cm)
\u6240\u4ee5
\u6bcd\u7ebf\u957f\u7ea6\u4e3a33.32(cm)\uff0c\u5c55\u5f00\u56fe\u5927\u6247\u5f62\u534a\u5f84\u7ea6\u4e3a45.96(cm)\uff0c\u5c0f\u6247\u5f62\u534a\u5f84\u7ea6\u4e3a12.64(cm)\uff0c\u6247\u5f62\u5706\u5fc3\u89d2\u7ea6\u4e3a156.65\u00b0
\u4fa7\u9762\u79ef=1/2 \uff08\u4e0a\u4e0b\u5e95\u5468\u957f\u4e4b\u548c\uff09*\u6bcd\u7ebf\u957f =\u03c0 \uff08R^2+r^2)
\u5373\u6bcd\u7ebf\u957f = \u03c0\uff08R^2+r^2) / \u03c0(R+r) = (R^2+r^2) / (R+r)
则π(R+r)L=πR²+πr²
L=(R²+r²)/(R+r)
绛旓細璁惧渾鍙扮殑姣嶇嚎闀夸负L 鍒蟺(R+r)L=蟺R²+蟺r²L=(R²+r²)/(R+r)
绛旓細姣嶇嚎闀跨害涓33.32(cm)锛屽睍寮鍥惧ぇ鎵囧舰鍗婂緞绾︿负45.96(cm)锛屽皬鎵囧舰鍗婂緞绾︿负12.64(cm)锛屾墖褰㈠渾蹇冭绾︿负156.65掳
绛旓細鍦嗗彴姣嶇嚎闀垮叕寮忔槸L=(R^2+r^2)/(R+r)銆傚渾鍙板悓鍦嗘煴鍜屽渾閿ヤ竴鏍蜂篃鏈夎酱銆佸簳闈佷晶闈㈠拰姣嶇嚎锛屽苟涓旂敤鍦嗗彴鍙拌酱鐨勫瓧姣嶈〃绀哄渾鍙般備竴銆佸渾鍙扮殑鐩稿叧闈笌绾 鍦嗗彴鐨勪晶闈細鏇查潰閮ㄥ垎绉颁负鍦嗗彴鐨勪晶闈傚渾鍙扮殑楂橈細涓や釜搴曢潰闂寸殑鍏瀭绾匡紝鍙仛鍦嗗彴鐨勯珮銆傚渾鍙扮殑姣嶇嚎锛氭棆杞殑鐩磋姊舰涓嶅瀭鐩翠簬搴曠殑鑵板彨鍋氬渾鍙扮殑姣嶇嚎銆傚渾鍙...
绛旓細鍏充簬鍦嗗彴姣嶇嚎闀跨殑璁＄畻鍏紡濡備笅锛渚ч潰绉=1/2锛堜笂涓嬪簳鍛ㄩ暱涔嬪拰锛*姣嶇嚎闀=蟺锛圧^2+r^2)鍗虫瘝绾块暱=蟺锛圧^2+r^2)/蟺(R+r)=(R^2+r^2)/(R+r)璧勬枡鎵╁睍锛氳绠楀渾鍙版瘝绾块暱鏄湪杩涜鍙樼數绔欒璁″伐浣滄椂锛岄潪甯搁噸瑕佺殑涓鐜紝鍥犱负姣嶇嚎闀垮害瀵瑰彉鐢电珯鐢电綉缁撴瀯鍙婄粍鎴愭湁鐫閲嶈鐨勫奖鍝嶃傚渾鍙版瘝绾块暱鐨勮绠楀叕寮忔槸...
绛旓細鏍规嵁棰樻剰锛岃鍦嗗彴鐨勪笂銆佷笅搴曢潰鍗婂緞鍜岄珮鍒嗗埆涓簒銆4x銆4x锛鍙緱姣嶇嚎闀夸负h2+(R?r)2=10锛屽嵆(4x)2+(4x?x)2=10锛岃В涔嬪緱x=2锛屾墍浠ュ渾鍙扮殑涓婂簳闈㈠崐寰勪负r=2锛屼笅搴曢潰鍗婂緞涓篟=8锛岄珮h=8锛庣敱姝ゅ彲寰楀渾鍙扮殑浣撶Н涓篤=13蟺h锛坮2+R2+rR锛=224蟺锛庢晠绛旀涓猴細224蟺锛庛
绛旓細鍦嗗彴鐨勪晶闈㈢Н鍏紡锛歋=蟺l锛圧+r锛夈鍦嗗彴鐨勬瘝绾块暱涓簂锛屼笂銆佷笅搴曢潰鍗婂緞鍒嗗埆涓簉銆丷銆傚渾鍙帮紙Frustum of a cone锛夊悓鍦嗘煴鍜屽渾閿ヤ竴鏍蜂篃鏈夎酱銆佸簳闈佷晶闈㈠拰姣嶇嚎锛屽苟涓旂敤鍦嗗彴鍙拌酱鐨勫瓧姣嶈〃绀哄渾鍙般傚渾閿ョ殑搴曢潰涓庢埅闈㈡槸鍦嗗彴鐨勫簳闈紝鍦嗛敟鐨勪晶闈㈠湪鎴潰涓庡簳闈箣闂寸殑閮ㄥ垎鏄渾鍙扮殑渚ч潰銆傚渾閿ョ殑姣嶇嚎鍦ㄦ埅闈笌搴曢潰...
绛旓細瑙ｏ細濡傚浘锛屾槸鍦嗗彴鎴潰鍥撅紝AD銆丅C鏄笂涓嬪簳鍗婂緞锛孉B鏄珮锛孋D鏄姣嶇嚎 杩嘍浣淒E鈯C 鍥犱负AB锛400(mm)锛孉D锛60(mm)锛孊C锛145(mm)鎵浠C锛145-60锛82(mm)鏍规嵁鍕捐偂瀹氱悊鍙緱DC鈮408.32(mm)璁惧皬鎵囧舰鍗婂緞涓篟锛屽垯澶ф墖褰㈠崐寰勪负R锛408.32 璁惧渾蹇冭搴︽暟涓篘锛屽垯鏈夛細60蟺锛漀蟺R/180 145蟺锛漀蟺(R锛...
绛旓細瀛愬崍鎴潰鍓栬鍥撅紝濡傚浘 鏍规嵁鍦嗗彴鐨勭壒寰侊紝AB//CD锛屽叾涓瑼B銆丆D鍒嗗埆涓轰笂搴曞渾鐨勭洿寰勫拰涓嬪簳鍦嗙殑鐩村緞锛孉D銆丅C涓鍦嗗彴鐨勬瘝绾锛孍D銆丒C涓哄渾閿ョ殑姣嶇嚎 鍒橝B=5.1锛孋D=6锛孉D=BC=10 EB/EC=AB/DC=5.1/6=17/20 鍒橞C/EC=1-EB/EC=3/20 鍒橢C=20/3路BC=200/3 鍗宠ˉ鍏ㄤ负鍦嗛敟鍚庯紝姣嶇嚎闀涓200/3 ...
绛旓細鍦嗗彴姣嶇嚎闀鐨勮绠楀叕寮忥細姣嶇嚎闀-2r+2h锛屽叾涓璻涓鍦嗗彴姣嶇嚎鐨澶栧崐寰勶紝h涓哄渾鍙版瘝绾跨殑楂樺害銆
绛旓細1銆佸凡鐭ヤ竴涓渾鍙扮殑楂樹负 8 cm锛屽簳闈㈠崐寰勪负 4 cm锛岄《闈㈠崐寰勪负 2 cm銆姹傚渾鍙扮殑姣嶇嚎闀銆傝В娉曪細鍦嗗彴鐨勬瘝绾块暱鍙敱鍕捐偂瀹氱悊璁＄畻锛屽嵆锛氭瘝绾块暱 = sqrt(楂榐2 + (搴曢潰鍗婂緞 - 椤堕潰鍗婂緞)^2)浠ｅ叆宸茬煡鏁版嵁锛屽緱锛氭瘝绾块暱 = sqrt(8^2 + (4 - 2)^2) = sqrt(68) 鈮 8.246 cm鍥犳锛岃鍦嗗彴鐨勬瘝绾...
