圆柱、圆锥、圆台、棱柱、棱台、棱锥、球、半球的体积和表面积！急需! 全汉字！只要公式！ 求棱柱、棱锥、棱台、圆柱、圆锥、圆台、球、的体积、侧面积、全...
\u68f1\u67f1.\u68f1\u9525.\u68f1\u53f0.\u5706\u67f1.\u5706\u9525.\u5706\u53f0.\u7403\u4f53\u7684\u5b9a\u4e49\u548c\u51e0\u4f55\u7279\u5f81\u7acb\u4f53\u51e0\u4f55
\u3000\u3000\u6570\u5b66\u4e0a\uff0c\u7acb\u4f53\u51e0\u4f55(solid geometry)\u662f3\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u7684\u51e0\u4f55\u7684\u4f20\u7edf\u540d\u79f0\u2014 \u56e0\u4e3a\u5b9e\u8df5\u4e0a\u8fd9\u5927\u81f4\u4e0a\u5c31\u662f\u6211\u4eec\u751f\u6d3b\u7684\u7a7a\u95f4\u3002\u4e00\u822c\u4f5c\u4e3a\u5e73\u9762\u51e0\u4f55\u7684\u540e\u7eed\u8bfe\u7a0b\u3002\u7acb\u4f53\u6d4b\u7ed8(Stereometry)\u5904\u7406\u4e0d\u540c\u5f62\u4f53\u7684\u4f53\u79ef\u7684\u6d4b\u91cf\u95ee\u9898\uff1a\u5706\u67f1,\u5706\u9525, \u5706\u53f0, \u7403, \u68f1\u67f1\uff0c\u68f1\u9525\u7b49\u7b49\u3002
\u3000\u3000\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b66\u6d3e\u5c31\u5904\u7406\u8fc7\u7403\u548c\u6b63\u591a\u9762\u4f53\uff0c\u4f46\u662f\u68f1\u9525\uff0c\u68f1\u67f1\uff0c\u5706\u9525\u548c\u5706\u67f1\u5728\u67cf\u62c9\u56fe\u5b66\u6d3e\u7740\u624b\u5904\u7406\u4e4b\u524d\u4eba\u4eec\u6240\u77e5\u751a\u5c11\u3002
\u3000\u3000\u5c24\u5f97\u585e\u65af(Eudoxus)\u5efa\u7acb\u4e86\u5b83\u4eec\u7684\u6d4b\u91cf\u6cd5\uff0c\u8bc1\u660e\u9525\u662f\u7b49\u5e95\u7b49\u9ad8\u7684\u67f1\u4f53\u79ef\u7684\u4e09\u5206\u4e4b\u4e00\uff0c\u53ef\u80fd\u4e5f\u662f\u7b2c\u4e00\u4e2a\u8bc1\u660e\u7403\u4f53\u79ef\u548c\u5176\u534a\u5f84\u7684\u7acb\u65b9\u6210\u6b63\u6bd4\u7684\u3002
[\u7f16\u8f91\u672c\u6bb5]\u7acb\u4f53\u51e0\u4f55\u57fa\u672c\u8bfe\u9898
\u3000\u3000\u5305\u62ec:
\u3000\u3000- \u9762\u548c\u7ebf\u7684\u91cd\u5408
\u3000\u3000- \u4e24\u9762\u89d2\u548c\u7acb\u4f53\u89d2
\u3000\u3000- \u65b9\u5757, \u957f\u65b9\u4f53, \u5e73\u884c\u516d\u9762\u4f53
\u3000\u3000- \u56db\u9762\u4f53\u548c\u5176\u4ed6\u68f1\u9525
\u3000\u3000- \u68f1\u67f1
\u3000\u3000- \u516b\u9762\u4f53, \u5341\u4e8c\u9762\u4f53, \u4e8c\u5341\u9762\u4f53
\u3000\u3000- \u5706\u9525\uff0c\u5706\u67f1
\u3000\u3000- \u7403
\u3000\u3000- \u5176\u4ed6\u4e8c\u6b21\u66f2\u9762: \u56de\u8f6c\u692d\u7403, \u692d\u7403, \u629b\u7269\u9762 \uff0c\u53cc\u66f2\u9762
\u3000\u3000\u516c\u7406
\u3000\u3000\u7acb\u4f53\u51e0\u4f55\u4e2d\u67094\u4e2a\u516c\u7406
\u3000\u3000\u516c\u74061 \u5982\u679c\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u4e24\u70b9\u5728\u4e00\u4e2a\u5e73\u9762\u5185\uff0c\u90a3\u4e48\u8fd9\u6761\u76f4\u7ebf\u5728\u6b64\u5e73\u9762\u5185\uff0e
\u3000\u3000\u516c\u74062 \u8fc7\u4e0d\u5728\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u4e09\u70b9\uff0c\u6709\u4e14\u53ea\u6709\u4e00\u4e2a\u5e73\u9762\uff0e
\u3000\u3000\u516c\u74063 \u5982\u679c\u4e24\u4e2a\u4e0d\u91cd\u5408\u7684\u5e73\u9762\u6709\u4e00\u4e2a\u516c\u5171\u70b9\uff0c\u90a3\u4e48\u5b83\u4eec\u6709\u4e14\u53ea\u6709\u4e00\u6761\u8fc7\u8be5\u70b9\u7684\u516c\u5171\u76f4\u7ebf\uff0e
\u3000\u3000\u516c\u74064 \u5e73\u884c\u4e8e\u540c\u4e00\u6761\u76f4\u7ebf\u7684\u4e24\u6761\u76f4\u7ebf\u5e73\u884c\uff0e
\u3000\u3000\u7acb\u65b9\u56fe\u5f62
\u3000\u3000\u7acb\u4f53\u51e0\u4f55\u516c\u5f0f
\u3000\u3000\u540d\u79f0 \u7b26\u53f7 \u9762\u79efS \u4f53\u79efV
\u3000\u3000\u6b63\u65b9\u4f53 a\u2014\u2014\u8fb9\u957f S\uff1d6a\uff3e\uff12\u3000V\uff1da\uff3e3
\u3000\u3000\u957f\u65b9\u4f53 a\u2014\u2014\u957f S\uff1d2(ab+ac+bc) V\uff1dabc
\u3000\u3000b\u2014\u2014\u5bbd
\u3000\u3000c\u2014\u2014\u9ad8
\u3000\u3000\u68f1\u67f1\u3000S\u2014\u2014\u5e95\u9762\u79ef \uff36\uff1d\uff33\uff48
\u3000\u3000h\u2014\u2014\u9ad8
\u3000\u3000\u68f1\u9525 S\u2014\u2014\u5e95\u9762\u79ef \uff36\uff1d\uff33\uff48\uff0f\uff13
\u3000\u3000h\u2014\u2014\u9ad8
\u3000\u3000\u68f1\u53f0 S1\u548cS2\u2014\u2014\u4e0a\u3001\u4e0b\u5e95\u9762\u79ef \uff36\uff1d\uff48\uff3b\uff33\uff11\uff0b\uff33\uff12\uff0b\u221a\uff08\uff33\uff11\uff3e\uff12\uff09\uff0f\uff12\uff3d\uff0f\uff13
\u3000\u3000h\u2014\u2014\u9ad8
\u3000\u3000\u62df\u67f1\u4f53 S1\u2014\u2014\u4e0a\u5e95\u9762\u79ef \uff36\uff1d\uff48\uff08\uff33\uff11\uff0b\uff33\uff12\uff0b\uff14\uff33\uff10\uff09\uff0f\uff16
\u3000\u3000S2\u2014\u2014\u4e0b\u5e95\u9762\u79ef
\u3000\u3000S0\u2014\u2014\u4e2d\u622a\u9762\u79ef
\u3000\u3000h\u2014\u2014\u9ad8
\u3000\u3000\u5706\u67f1 r\u2014\u2014\u5e95\u534a\u5f84 \uff23\uff1d\uff12\u03c0\uff52\u3000\uff36\uff1d\uff33\u5e95\uff48=\u03a0rh
\u3000\u3000h\u2014\u2014\u9ad8
\u3000\u3000C\u2014\u2014\u5e95\u9762\u5468\u957f
\u3000\u3000S\u5e95\u2014\u2014\u5e95\u9762\u79ef \uff33\u5e95\uff1d\u03c0\uff32\uff3e\uff12
\u3000\u3000S\u4fa7\u2014\u2014\u4fa7\u9762\u79ef \uff33\u4fa7\uff1d\uff23\uff48
\u3000\u3000S\u8868\u2014\u2014\u8868\u9762\u79ef \uff33\u8868\uff1d\uff23\uff48\uff0b\uff12\uff33\u5e95
\u3000\u3000S\u5e95\uff1d\u03c0r\uff3e2
\u3000\u3000\u7a7a\u5fc3\u5706\u67f1 R\u2014\u2014\u5916\u5706\u534a\u5f84
\u3000\u3000r\u2014\u2014\u5185\u5706\u534a\u5f84
\u3000\u3000h\u2014\u2014\u9ad8 V\uff1d\u03c0h(R\uff3e\uff12-r\uff3e2)
\u3000\u3000\u76f4\u5706\u9525 r\u2014\u2014\u5e95\u534a\u5f84
\u3000\u3000h\u2014\u2014\u9ad8 V\uff1d\u03c0r\uff3e\uff12h/3
\u3000\u3000\u5706\u53f0 r\u2014\u2014\u4e0a\u5e95\u534a\u5f84
\u3000\u3000R\u2014\u2014\u4e0b\u5e95\u534a\u5f84
\u3000\u3000h\u2014\u2014\u9ad8 V\uff1d\u03c0h(R\uff3e2\uff0bRr\uff0br\uff3e2)/3
\u3000\u3000\u7403 r\u2014\u2014\u534a\u5f84
\u3000\u3000d\u2014\u2014\u76f4\u5f84 V\uff1d4/3\u03c0r\uff3e3\uff1d\u03c0d\uff3e2/6
\u3000\u3000\u7403\u7f3a h\u2014\u2014\u7403\u7f3a\u9ad8
\u3000\u3000r\u2014\u2014\u7403\u534a\u5f84
\u3000\u3000a\u2014\u2014\u7403\u7f3a\u5e95\u534a\u5f84 a\uff3e2\uff1dh(2r-h) V\uff1d\u03c0h(3a\uff3e2+h\uff3e2)/6 \uff1d\u03c0h2(3r-h)/3
\u3000\u3000\u7403\u53f0 r1\u548cr2\u2014\u2014\u7403\u53f0\u4e0a\u3001\u4e0b\u5e95\u534a\u5f84
\u3000\u3000h\u2014\u2014\u9ad8 V\uff1d\u03c0h[3(r12\uff0br22)+h2]/6
\u3000\u3000\u5706\u73af\u4f53 R\u2014\u2014\u73af\u4f53\u534a\u5f84
\u3000\u3000D\u2014\u2014\u73af\u4f53\u76f4\u5f84
\u3000\u3000r\u2014\u2014\u73af\u4f53\u622a\u9762\u534a\u5f84
\u3000\u3000d\u2014\u2014\u73af\u4f53\u622a\u9762\u76f4\u5f84 V\uff1d2\u03c0\uff3e2Rr\uff3e2 \uff1d\u03c0\uff3e2Dd\uff3e2/4
\u3000\u3000\u6876\u72b6\u4f53 D\u2014\u2014\u6876\u8179\u76f4\u5f84
\u3000\u3000d\u2014\u2014\u6876\u5e95\u76f4\u5f84
\u3000\u3000h\u2014\u2014\u6876\u9ad8 V\uff1d\u03c0h(2D\uff3e2\uff0bd2\uff3e)/12 (\u6bcd\u7ebf\u662f\u5706\u5f27\u5f62,\u5706\u5fc3\u662f\u6876\u7684\u4e2d\u5fc3)
\u3000\u3000V\uff1d\u03c0h(2D\uff3e2\uff0bDd\uff0b3d\uff3e2/4)/15 (\u6bcd\u7ebf\u662f\u629b\u7269\u7ebf\u5f62)
\u3000\u3000\u6ce8\uff1a\u521d\u5b66\u8005\u4f1a\u8ba4\u4e3a\u7acb\u4f53\u51e0\u4f55\u5f88\u96be\uff0c\u4f46\u53ea\u8981\u6253\u597d\u57fa\u7840\uff0c\u7acb\u4f53\u51e0\u4f55\u5c06\u4f1a\u53d8\u5f97\u5f88\u5bb9\u6613\u3002\u5b66\u597d\u7acb\u4f53\u51e0\u4f55\u6700\u5173\u952e\u7684\u5c31\u662f\u5efa\u7acb\u8d77\u7acb\u4f53\u6a21\u578b\uff0c\u628a\u7acb\u4f53\u8f6c\u6362\u4e3a\u5e73\u9762\uff0c\u8fd0\u7528\u5e73\u9762\u77e5\u8bc6\u6765\u89e3\u51b3\u95ee\u9898\uff0c\u7acb\u4f53\u51e0\u4f55\u5728\u9ad8\u8003\u4e2d\u80af\u5b9a\u4f1a\u51fa\u73b0\u4e00\u9053\u5927\u9898\uff0c\u6240\u4ee5\u5b66\u597d\u7acb\u4f53\u662f\u975e\u5e38\u5173\u952e\u7684\u3002
\u8f6c\u81ea\u767e\u5ea6\u8bcd\u6761\uff0c\u8c22\u8c22\u91c7\u7eb3
\u67f1\u4f53\u4f53\u79efV=Sh
\u53f0\u4f53V=1/3(S+S'+JSS')h
\u690e\u4f53V=1/3Sh
\u9762\u79ef\uff1a
\u591a\u9762\u4f53\uff1a\u6240\u6709\u9762\u9762\u79ef\u603b\u548c\uff08\u4e0d\u9700\u8981\u8bb0\u516c\u5f0f\uff09
\u65cb\u8f6c\u4f53\uff1a\u53ea\u9700\u8981\u77e5\u9053\u4fa7\u9762\u5c55\u5f00\u662f\u4ec0\u4e48\u5c31\u53ef\u4ee5\uff0c\u4e5f\u4e0d\u9700\u8981\u8bb0\u516c\u5f0f
\u5706\u62c4\uff1a\u4fa7\u9762\u662f\u77e9\u5f62
\u5706\u9525\uff1a\u6247\u5f62\uff08\u5f53\u4e09\u89d2\u5f62\u9762\u79ef\u6765\u7b97~\uff09
\u5706\u53f0\uff1a\u6247\u73af\uff08\u5f53\u68af\u5f62\u9762\u79ef\u7b97\uff09
\u7403\uff1a
V=4/3paiR^3
S=4paiR^2
\u6ce8\u610fS--\u5e95\u9762\u79ef
pai=3.1415....
R\u8868\u793a\u534a\u5f84
h\u8868\u793a\u9ad8
台体V=1/3(S+S'+JSS')h
椎体V=1/3Sh
面积：
多面体：所有面面积总和（不需要记公式）
旋转体：只需要知道侧面展开是什么就可以，也不需要记公式
圆拄：侧面是矩形
圆锥：扇形（当三角形面积来算~）
圆台：扇环（当梯形面积算）
球：
V=4/3paiR^3
S=4paiR^2
注意S--底面积
pai=3.1415....
R表示半径
h表示高
柱体体积V=Sh
台体V=1/3(S+S'+JSS')h
椎体V=1/3Sh
面积：
多面体：所有面面积总和（不需要记公式）
旋转体：只需要知道侧面展开是什么就可以，也不需要记公式
圆拄：侧面是矩形
圆锥：扇形（当三角形面积来算~）
圆台：扇环（当梯形面积算）
球：
V=4/3paiR^3
S=4paiR^2
注意S--底面积
pai=3.1415....
R表示半径
h表示高
绛旓細鏌变綋浣撶НV=Sh 鍙颁綋V=1/3(S+S'+JSS')h 妞庝綋V=1/3Sh 闈㈢Н锛氬闈綋锛氭墍鏈夐潰闈㈢Н鎬诲拰锛堜笉闇瑕佽鍏紡锛夋棆杞綋锛氬彧闇瑕佺煡閬撲晶闈㈠睍寮鏄粈涔堝氨鍙互锛屼篃涓嶉渶瑕佽鍏紡 鍦嗘媱锛氫晶闈㈡槸鐭╁舰 鍦嗛敟锛氭墖褰紙褰撲笁瑙掑舰闈㈢Н鏉ョ畻~锛鍦嗗彴锛氭墖鐜紙褰撴褰㈤潰绉畻锛夌悆锛歏=4/3paiR^3 S=4paiR^2 娉ㄦ剰S--搴曢潰绉 pai...
绛旓細锛氱偣鍒 姝ｅ杈瑰舰 涓績澶т簬闆惰窛绂荤殑鎷変几鎵鏋勬垚鐨 鍑犱綍浣 锛鍦嗛敟锛氱偣鍒版鍦嗗舰鍦嗗績澶т簬闆惰窛绂荤殑鎷変几鎵鏋勬垚鐨勫嚑浣曚綋锛妫辨煴锛氭澶氳竟褰㈤珮搴﹀ぇ浜庨浂鐨勬鍙嶆柟鍚戝瀭鐩存媺浼告墍鏋勬垚鐨勫嚑浣曚綋锛鍦嗘煴锛氭鍦嗗舰楂樺害澶т簬闆剁殑姝ｅ弽鏂瑰悜鍨傜洿鎷変几鎵鏋勬垚鐨勫嚑浣曚綋锛妫卞彴 锛氶潪鐩哥瓑鐩镐技姝ｅ杈瑰舰澶т簬闆惰窛绂荤殑鎷変几鎵鏋勬垚鐨勫嚑浣曚綋锛鍦嗗彴 锛...
绛旓細鏌变綋浣撶НV=Sh 鍙颁綋V=1/3(S+S'+JSS')h 妞庝綋V=1/3Sh 闈㈢Н锛氬闈綋锛氭墍鏈夐潰闈㈢Н鎬诲拰锛堜笉闇瑕佽鍏紡锛夋棆杞綋锛氬彧闇瑕佺煡閬撲晶闈㈠睍寮鏄粈涔堝氨鍙互锛屼篃涓嶉渶瑕佽鍏紡 鍦嗘媱锛氫晶闈㈡槸鐭╁舰 鍦嗛敟锛氭墖褰紙褰撲笁瑙掑舰闈㈢Н鏉ョ畻~锛鍦嗗彴锛氭墖鐜紙褰撴褰㈤潰绉畻锛夌悆锛歏=4/3paiR^3 S=4paiR^2 娉ㄦ剰S--搴曢潰绉 pai...
绛旓細妫遍敟锛氱偣鍒版澶氳竟褰腑蹇冨ぇ浜庨浂璺濈鐨勬媺浼告墍鏋勬垚鐨勫嚑浣曚綋锛鍦嗛敟锛氱偣鍒版鍦嗗舰鍦嗗績澶т簬闆惰窛绂荤殑鎷変几鎵鏋勬垚鐨勫嚑浣曚綋锛妫辨煴锛氭澶氳竟褰㈤珮搴﹀ぇ浜庨浂鐨勬鍙嶆柟鍚戝瀭鐩存媺浼告墍鏋勬垚鐨勫嚑浣曚綋锛鍦嗘煴锛氭鍦嗗舰楂樺害澶т簬闆剁殑姝ｅ弽鏂瑰悜鍨傜洿鎷変几鎵鏋勬垚鐨勫嚑浣曚綋锛妫卞彴锛氶潪鐩哥瓑鐩镐技姝ｅ杈瑰舰澶т簬闆惰窛绂荤殑鎷変几鎵鏋勬垚鐨勫嚑浣曚綋锛鍦嗗彴锛氱浉闈...
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