一个正三棱台的上下底面边长为3cm和6cm，侧面高为根号3，求三棱台体积
\u4e00\u4e2a\u6b63\u4e09\u68f1\u53f0\u7684\u4e0a\u4e0b\u5e95\u9762\u8fb9\u957f\u4e3a3cm\u548c6cm\uff0c\u4fa7\u9762\u9ad8\u4e3a\u6839\u53f73\uff0c\u6c42\u4e09\u68f1\u53f0\u4f53\u79ef\u6839\u636e\u7b49\u8fb9\u4e09\u89d2\u5f62\u9762\u79ef=\u221a3/4*\u8fb9\u957f*\u8fb9\u957f
\u4e09\u68f1\u53f0\u4f53\u79ef = \u221a3/8*(3^2+6^2)*\u221a3
=16.875cm^3
\u6613\u77e5\u3001\u659c\u9ad8\uff1d\u221a3\uff0c\u4fa7\u68f1\uff1d2.\u5982\u56fe \u4e09\u68f1\u53f0\u7684\u6b63\u622a\u9762\u3002
\u9ad8 H²\uff1d2²+\uff08\u221a3-x\uff09²\uff1d\uff08\u221a3\uff09²-x². x\uff1d1/\u221a3. H\uff1d2\u221a6/3.
\u4f53\u79efV\uff1d\uff081/3\uff09\uff082\u221a6/3\uff09\uff08\u221a3/4\uff09[1+9+\u221a3]\uff1d5\u221a2/3+\u221a6/6
\u22482.765\uff08\u4f53\u79ef\u5355\u4f4d\uff09
三棱台体积 = √3/8*(3^2+6^2)*√3
=16.875cm^3
绛旓細瑙ｏ細鈭垫槸姝ｄ笁妫卞彴 涓婂簳闈鍜屼笅鍦伴潰鍧囦负姝ｄ笁瑙掑舰 涓婂簳闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=鈭3 涓嬪湴闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=2鈭3 鈭翠笂涓嬭窛绂诲樊 锛 2鈭3-鈭3=鈭3 鈭存１闀=鈭歔(鈭3)�0�5+楂�0�5]=鈭21/2 涓婂簳闈㈢瓑杈光柍涓績鍒...
绛旓細瑙ｏ細鈭鏄涓夋１鍙 涓婂簳闈㈠拰涓嬪湴闈㈠潎涓烘涓夎褰 涓婂簳闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=鈭3 涓嬪湴闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=2鈭3 鈭翠笂涓嬭窛绂诲樊 锛 2鈭3-鈭3=鈭3 鈭妫遍暱=鈭歔(鈭3)??+楂??]=鈭21/2 涓婂簳闈㈢瓑杈光柍涓績鍒拌竟鐨勮窛绂 锛 杈归暱梅2鈭3=鈭3/2 涓嬪湴闈㈢瓑...
绛旓細瑙ｏ細鈭垫槸姝ｄ笁妫卞彴 涓婂簳闈鍜屼笅鍦伴潰鍧囦负姝ｄ笁瑙掑舰 涓婂簳闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=鈭3 涓嬪湴闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=2鈭3 鈭翠笂涓嬭窛绂诲樊 锛 2鈭3-鈭3=鈭3 鈭存１闀=鈭歔(鈭3)�0�5 楂�0�5]=鈭21/2 涓婂簳闈㈢瓑杈光柍涓績鍒...
绛旓細涓婂簳闈㈠拰涓嬪湴闈㈠潎涓烘涓夎褰 涓婂簳闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=鈭3 涓嬪湴闈㈢瓑杈光柍涓績鍒扮鐐圭殑璺濈 锛 杈归暱梅鈭3=2鈭3 鈭翠笂涓嬭窛绂诲樊 锛 2鈭3-鈭3=鈭3 鈭妫遍暱=鈭歔(鈭3)²+楂²]=鈭21/2 涓婂簳闈㈢瓑杈光柍涓績鍒拌竟鐨勮窛绂 锛 杈归暱梅2鈭3=鈭3/2 涓嬪湴闈㈢瓑杈光柍涓績鍒...
绛旓細渚ч珮=鏍瑰彿{(3/2)^2+[(6-3)/2]^2}=3鏍2/2 渚ч潰绉=4*(3鏍2/2)*(6+3)/2=27鏍瑰彿2 琛ㄩ潰绉=渚ч潰绉+涓婁笅搴闈㈢Н=27鏍2+3*3+6*6=45+27鏍2 浣撶Н鍏紡浠ｅ叆鍗冲彲
绛旓細鏍规嵁 绛夎竟涓夎褰 闈㈢Н=鈭3/4*杈归暱*杈归暱 涓夋１鍙 浣撶Н = 鈭3/8*(3^2+6^2)*鈭3 =16.875cm^3
绛旓細瑙ｏ細渚ч珮=鏍瑰彿{(3/2)^2+[(6-3)/2]^2}=3鏍2/2 渚ч潰绉=4*(3鏍2/2)*(6+3)/2=27鏍瑰彿2
绛旓細.(1)涓夋１鍙版枩楂樹负 cm(2)锛屼晶闈㈢Н涓 cm 2 锛岃〃闈㈢Н涓 cm 2 . (1)璁綩 1 銆丱鍒嗗埆涓姝ｄ笁妫卞彴ABC鈥擜 1 B 1 C 1 鐨勪笂銆佷笅搴曢潰姝ｄ笁瑙掑舰鐨勪腑蹇冿紝濡傚浘锛屽垯O 1 O= 锛岃繃O 1 浣淥 1 D 1 鈯 1 C 1 锛孫D鈯C锛屽垯D 1 D涓烘枩楂橈紱杩嘍 1 浣淒 1 E鈯D浜嶦锛屽垯D...
绛旓細鍏抽敭鏄眰鍑烘枩楂
绛旓細绛旓細濡備笅鍥撅紝姝ｄ笁瑙掑舰ABC杈归暱涓6锛屾涓夎褰EF杈归暱涓3 姝ｄ笁妫卞彴楂榟=2锛岃姝ｄ笁妫遍敟O-ABC鐨勯珮涓篐锛屽垯姝ｄ笁妫遍敟O-DEF鐨勯珮涓篐-h 鏍规嵁鐩镐技鎬ц川鏈夛細(H-h)/H=DE/AB=3/6=1/2 (H-2)/H=1/2 瑙ｅ緱锛欻=4 姝ｄ笁瑙掑舰ABC搴曡竟涓婄殑楂=6sin60掳=3鈭3 椤剁偣C鍒板簳闈腑蹇冪殑璺濈=2鈭3 鏍规嵁鍕捐偂...
