正四面体的外接球内切球棱切球公式 棱长为a的正四面体的外接球、内接球、棱切球半径计算公式为什么...
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高是√6a/3,外接球半径√6a/4,内切球半径√6a/12，棱切球半径√2a/4绛旓細楂樻槸鈭6a/3,澶栨帴鐞鍗婂緞鈭6a/4,鍐呭垏鐞鍗婂緞鈭6a/12锛妫卞垏鐞鍗婂緞鈭2a/4
绛旓細鍥炵瓟锛澶栨帴鐞鍗婂緞:a鐨勫钩鏂瑰姞a鐨勫钩鏂圭殑鍜屽啀寮浜屾鏂,鍐呮帴鐞冨崐寰:鍗冲崐寰勪负a,妫鎺ョ悆鐨勫簲璇ュ拰鍐呮帴鐞冪殑涓鏍峰惂!甯屾湜閲囩撼銆
绛旓細5. 澶栨帴鐞冿細姝ｅ洓闈綋鐨勫鎺ョ悆鍗婂緞涓衡垰6a/4銆傚畠鐨勪綋绉腑锛屾鍥涢潰浣撴墍鍗犳瘮渚嬬害涓12.2517532%锛屽叿浣撹绠椾负姝ｅ洓闈綋浣撶Н闄や互澶栨帴鐞冧綋绉殑2*鈭3/9*蟺銆6. 鍐呭垏鐞锛氬唴鍒囩悆鍗婂緞涓衡垰6a/12锛屽唴鍒囩悆浣撶Н鍗犳鍥涢潰浣撲綋绉殑姣斾緥涓合*鈭3/18锛岀害30.2299894%銆7. 妫卞垏鐞锛氭１鍒囩悆鍗婂緞涓衡垰2a/4锛岃繖鏄垏...
绛旓細鑻ユ１闀夸负a锛屽鍒囩悆鍗婂緞涓衡垰6a/4锛屽唴鍒囩悆鍗婂緞涓衡垰6a/12銆傝姝ｅ洓闈綋鏄疭锛岮BC锛岃繃鐐筍浣滈珮绾縎H浜ゅ簳闈BC浜庣偣H锛屽垯鍐呭垏鐞冪悆蹇冨湪SH涓婏紝璁惧叾鍗婂緞鏄疪锛屽垯涓昏灏变骇鐢熷洓涓洓闈綋锛氭．鏃廜锛峉AB銆丱锛峉BC銆丱锛峉CA銆丱锛岮BC锛岃繖鍥涗釜鍥涢潰浣撶殑楂橀兘鏄唴鍒囩悆鐨勫崐寰凴锛屽簳闈㈤兘鏄互a涓鸿竟闀挎槸姝ｄ笁瑙掑舰锛屽埄鐢...
绛旓細楂橈細鈭6a/3銆備腑蹇冩妸楂樺垎涓1:3涓ら儴鍒嗐傝〃闈㈢Н锛氣垰3a^2 浣撶Н锛氣垰2a^3/12 瀵规１涓偣鐨勮繛绾挎鐨勯暱锛氣垰2a/2 澶栨帴鐞鍗婂緞锛氣垰6a/4锛姝ｅ洓闈綋浣撶Н鍗犲鎺ョ悆浣撶Н鐨2*3^0.5/9*蟺锛岀害12.2517532%銆鍐呭垏鐞鍗婂緞锛氣垰6a/12锛屽唴鍒囩悆浣撶Н鍗犳鍥涢潰浣撲綋绉殑蟺*3^0.5/18锛岀害30.2299894%銆妫卞垏鐞鍗婂緞...
绛旓細姝ｅ洓闈綋鐨閲嶅績,鍥涙潯楂樼殑浜ょ偣,澶栨帴鐞冨唴鍒囩悆鐞蹇冨叡鐐.姝ｅ洓闈綋鏈変竴涓湪鍏跺唴閮ㄧ殑鍐呭垏鐞冨拰涓冧釜鏃佸垏鐞冧笌鍥涗釜闈㈢浉鍒,鍏朵腑鏈変笁涓梺鍒囩悆鐞蹇冨湪鏃犵┓杩滃.姝ｅ洓闈綋鏈夊洓鏉′笁閲嶆棆杞绉拌酱,鍏釜瀵圭О闈.姝ｅ洓闈綋鍙笌姝ｅ叓闈綋濉弧绌洪棿,鍦ㄤ竴鐐瑰懆鍥存湁鍏釜姝ｅ洓闈綋鍜屽叚涓鍏潰浣.椤剁偣鏁:4 (鐩稿悓) 妫辨暟:6 ...
绛旓細鍐呭垏鐞冨崐寰勪负12鍒嗕箣鏍瑰彿6鍊峚;澶栨帴鐞冨崐寰9鍒嗕箣鏍瑰彿6鍊峚 姝ｅ洓闈綋澶栨帴鐞冪悆蹇冧笌鍐呭垏鐞冪悆蹇冩槸鍦ㄥ悓涓鐐逛笂锛岃岃繖涓鐐规槸鍥涢潰浣撳叾涓袱骞抽潰浣滃瀭绾跨殑浜ょ偣o銆傚彲鐢ㄦ埅闈㈡柟娉曟眰鍑哄瀭绾块暱搴涓轰笁鍒嗕箣鏍瑰彿6鍊峚銆傜劧鍚庢妸鍥涢潰浣撶湅鎴愮敱鍥涗釜鐩哥瓑鐨勫皬涓夋１閿ワ紙浜ょ偣o鍑哄彂鍚鍥涢潰浣撶殑涓変釜椤剁偣寮曞嚭涓夋潯绾匡紝鎶婂洓闈綋鍒嗘垚鍥涗唤...
绛旓細姝ｅ洓闈綋鐨勫鎺ョ悆鍗婂緞鍏紡R=(鈭6)a/4銆1銆佹涓夋１閿ュ鎺ョ悆蹇冨湪椤剁偣涓庡簳闈㈤噸蹇冪殑杩炵嚎鐨勮窛搴曢潰1/4澶勩傚拰璁＄畻鍐呭垏鐞蹇冧竴鏍风畻鍑哄渾蹇冩墍鍦ㄧ洿绾匡紙鍗抽《鐐逛笌搴曢潰閲嶅績鐨勮繛绾匡級鐨勯暱搴︼紝鍗冲彲绠楀嚭椤剁偣涓庣悆蹇冪殑璺濈锛堝嵆澶栨帴鐞冨崐寰勶級銆2銆侀暱鏂逛綋鐨勫鎺ョ悆鍗婂緞锛2r锛²=a²+b²+c²...
绛旓細1銆澶栨帴鐞銆傝竟闀夸负a鐨姝ｅ洓闈綋鍙互鐪嬫垚鏄竟闀挎槸(鈭2/2)a鐨勬鏂逛綋鎴嚭鏉ョ殑锛屽垯鍏跺鎺ョ悆鐩村緞鏄鏂逛綋杈归暱鐨勨垰3鍊嶃2銆佸唴鍒囩悆鍗婂緞銆傝姝ｅ洓闈綋鏄疭锛岮BC锛岃繃鐐筍浣滈珮绾縎H浜ゅ簳闈BC浜庣偣H锛屽垯鍐呭垏鐞冪悆蹇冨湪SH涓婏紝璁惧叾鍗婂緞鏄疪锛屽垯涓昏灏变骇鐢熷洓涓洓闈綋锛歄锛峉AB銆丱锛峉BC銆丱锛峉CA銆丱锛岮BC锛岃繖鍥...
绛旓細1銆佹鏂浣撶殑鍐呭垏鐞锛氭寚鐨勬槸鐞冧笌姝ｆ柟浣撶殑鍚勪釜闈㈢浉鍒囷紝鑰屼笖杩欎釜鐞冩槸澶勪簬姝ｆ柟浣撳唴閮ㄧ殑銆2銆佹鏂逛綋鐨勫鎺ョ悆锛氭寚鐨勬槸鐞冨浜庢鏂逛綋鐨勫閮紝鑰屼笖姝ｆ柟浣撶殑鍚勪釜瀹氱偣閮藉湪鐞冮潰涓娿3銆佹鏂浣撶殑妫卞垏鐞锛氭１鍒囩悆涔熸槸澶勪簬姝ｆ柟浣撶殑澶栭儴锛屼絾瀹冩槸鍜屾鏂逛綋鐨勫悇鏉℃１閮界浉鍒囥
