怎么计算圆台体积(文字公式)
\u5706\u53f0\u4f53\u79ef\u600e\u4e48\u7b97\uff08\u516c\u5f0f\uff09\u8bbe\u4e0a\u5e95\u9762\u79efS\u4e0a\uff0c\u4e0b\u5e95\u9762\u79efS\u4e0b\uff0c\u9ad8\u4e3aH\uff0c\u90a3\u4e2a\u6d3e\u5c31\u7528PI\u8868\u793a\u5427\uff0c\u5706\u53f0\u4f53\u79ef\u8868\u793a\u4e3a\uff1a
V\u5706\u53f0=1/3*PI*H*\uff08S\u4e0a+S\u4e0b+\u6839\u53f7\uff08S\u4e0a*S\u4e0b\uff09\uff09
V=1/3\u03c0h\uff08r²\uff0bR²\uff0brR\uff09
\u89e3\u91ca\uff1a\u5706\u53f0\u7684\u4e0a\u3001\u4e0b\u5e95\u9762\u7684\u534a\u5f84\u5206\u522b\u662fr\uff0cR\uff0c\u9ad8\u662fh
\u5706\u53f0\u6027\u8d28\uff1a
1\u3001\u5e73\u884c\u4e8e\u5e95\u9762\u7684\u622a\u9762\u662f\u5706\u3002
2\u3001\u8fc7\u8f74\u7684\u622a\u9762\u662f\u7b49\u8170\u68af\u5f62\u3002
3\u3001\u540c\u522b\u7684\u68f1\u53f0\u4e00\u6837\uff0c\u82e5\u5b83\u662f\u4e00\u4e2a\u5706\u9525\u4f53\u5728½\u5904\u622a\u65ad\uff0c\u5219\u4e0a\u5e95\u534a\u5f84\u4e5f\u5e94\u4e3a\u4e0b\u5e95\u76841/2\uff0c\u622a\u4e0b\u9762\u79ef\u662f\u6574\u4e2a\u5706\u9525\u9762\u79ef\u76841/7\u8fc7\u5706\u53f0\u4fa7\u9762\u4e00\u70b9\u6709\u4e14\u53ea\u6709\u4e00\u6761\u6bcd\u7ebf\u3002
4\u3001\u5982\u679c\u6cbf\u4e00\u4e2a\u76f4\u89d2\u68af\u5f62\u5782\u76f4\u4e8e\u5e95\u8fb9\u7684\u8170\u65cb\u8f6c\u4e00\u5468\uff0c\u5c06\u5f97\u5230\u4e00\u4e2a\u5706\u53f0\u3002
5\u3001\u5706\u53f0\u4efb\u610f\u4e24\u6761\u6bcd\u7ebf\u5ef6\u957f\u540e\u4ea4\u4e8e\u4e00\u70b9\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5706\u53f0\u76f8\u5173\u51e0\u4f55\u56fe\u5f62\uff1a\u5706\u9525
\u5706\u9525\u9762\u548c\u4e00\u4e2a\u622a\u5b83\u7684\u5e73\u9762\uff08\u6ee1\u8db3\u4ea4\u7ebf\u4e3a\u5706\uff09\u7ec4\u6210\u7684\u7a7a\u95f4\u51e0\u4f55\u56fe\u5f62\u53eb\u5706\u9525\u3002
\u4ee5\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u76f4\u89d2\u8fb9\u6240\u5728\u76f4\u7ebf\u4e3a\u65cb\u8f6c\u8f74\uff0c\u5176\u4f59\u4e24\u8fb9\u65cb\u8f6c\u800c\u6210\u7684\u66f2\u9762\u6240\u56f4\u6210\u7684\u51e0\u4f55\u4f53\u53eb\u505a\u5706\u9525\u3002
\u6ce8\u610f\uff1a\u5706\u9525\u4e0d\u662f\u7279\u6b8a\u7684\u5706\u67f1\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u5706\u9525
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u5706\u53f0
圆台高为H，底面（大的）半径为R，底面（小的）半径为r。派 我用手机打不出来，用符号@代替。
V=H@/(3R-3r) × (R^3-r^3)
~O(∩_∩)O
大圆锥减小圆锥 不妨设大小的半径高分别为r1 r2 h1 h2 V台＝三分之一派（r1方×h1·r2方h2）
绛旓細浣撶Н = (1/3)蟺[(r1^2 + r2^2 + 鈭(r1^2 * r2^2)) * h]鍏朵腑锛歳1 鏄渾鍙扮殑涓婂崐寰勶紱r2 鏄渾鍙扮殑涓嬪崐寰勶紱h 鏄渾鍙扮殑楂樺害銆傛暟瀛 鍦嗗彴浣撶Н璁＄畻涓句緥 璁╂垜浠妇涓緥瀛愭潵璇存槑濡備綍浣跨敤杩欎釜鍏紡銆傚亣璁炬垜浠湁涓涓渾鍙帮紝涓婂崐寰勪负 5 鍘樼背锛屼笅鍗婂緞涓 10 鍘樼背锛岄珮搴︿负 10 鍘樼背銆傛垜浠彲浠ョ敤浠ヤ笅姝ラ...
绛旓細鍦嗗彴鐨勪綋绉叕寮忥細锛鍏朵腑r鏄笂搴曢潰鍗婂緞锛孯鏄笅搴曢潰鍗婂緞銆傚渾鍙扮殑琛ㄩ潰绉叕寮忥細S=蟺r²+蟺R²+蟺Rl+蟺rl=蟺(r²+R²+Rl+rl)r锛嶄笂搴曞崐寰勩丷锛嶄笅搴曞崐寰勩乭锛嶉珮銆乴鈥旀瘝绾=鏍瑰彿涓媅锛圧-r锛²+h²]鍦嗗彴鐨勫簳闈㈠拰椤堕潰杩戜技鏃讹紝鍦嗗彴浣撶Н鍙繎浼间负锛氬渾鍙扮殑搴曢潰闈㈢НS1...
绛旓細鍦嗗彴鐨勪綋绉叕寮忎负V=(1/3)蟺h(r^2+R^2+Rr)锛宧鏄渾鍙扮殑楂橈紝r鍜孯鏄渾鍙颁笂涓嬪簳闈㈢殑鍗婂緞銆備竴銆佸渾鍙扮殑瀹氫箟 鐢ㄤ竴涓钩琛屼簬鍦嗛敟搴曢潰鐨勫钩闈㈠幓鎴渾閿ワ紝搴曢潰涓庢埅闈箣闂寸殑閮ㄥ垎鍙仛鍦嗗彴銆備簩銆佸渾鍙扮殑鎬ц川 1銆佸钩琛屼簬搴曢潰鐨勬埅闈㈡槸鍦嗐2銆佽繃杞寸殑鎴潰鏄瓑鑵版褰3銆佸悓鍒殑妫卞彴涓鏍凤紝鑻ュ畠鏄竴涓渾閿ヤ綋鍦&...
绛旓細鎬讳箣锛鍦嗗彴浣撶Н鍏紡涓篤 = (1/3)πh(R² + Rr + r²)锛屽畠鏄氳繃鍑犱綍瀛﹀拰绉垎璁＄畻鎺ㄥ寰楀埌鐨銆傝繖涓叕寮忓彲浠ユ柟渚垮湴璁＄畻鍦嗗彴鐨勪綋绉紝骞朵笖鍦ㄧ壒娈婃儏鍐典笅鍙互绠鍖栦负鍦嗘煴浣撳拰鍦嗛敟浣撶殑浣撶Н鍏紡銆
绛旓細鍦嗗彴浣撶Н鍏紡锛氬叕寮忎腑r涓轰笂搴曞崐寰勩丷涓轰笅搴曞崐寰勩乭涓洪珮銆傚渾閿ヤ綋鐨勪綋绉細 V=1/3 * 蟺 * h * r^2 鍋囪锛屽渾鍙板簳闈㈠崐寰勪负 R 锛岄《闈㈠崐寰勪负 r 锛屽彴楂 h 锛 鍒欏亣璁剧殑澶у渾閿ヤ綋绉 V1=1/3 * 蟺 * h1 * R^2 锛涘皬鍦嗛敟鐨勪綋绉 V2=1/3 * 蟺 * h2 * r^2 锛屾槑鏄 r锛歊 = h2锛歨1...
绛旓細鍦嗗彴鐨勪綋绉叕寮忔槸V= [S+S鈥+鈭 (SS鈥)]h梅3=蟺h (R^2+Rr+r^2)/3锛鍏紡涓璻涓轰笂搴曞崐寰勩丷涓轰笅搴曞崐寰勩乭涓洪珮銆傚渾鍙帮紙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〃绀哄渾鍙般傜敤涓涓钩琛屼簬鍦嗛敟搴曢潰鐨勫钩闈㈠幓鎴渾閿ワ紝搴曢潰涓庢埅闈箣闂寸殑閮ㄥ垎鍙仛鍦嗗彴...
绛旓細鍦嗗彴鐨浣撶Н璁＄畻鍏紡涓猴細V=蟺h锛圧1^2+R2^2+R1*R2锛夈傚叾涓環涓哄渾鍙伴珮搴︼紝R1鍜孯2鍒嗗埆涓哄渾鍙扮殑涓婂簳鍜屼笅搴曞崐寰勩傚渾鍙扮殑浣撶Н鍙互鐪嬩綔鏄敱涓や釜鍦嗛敟缁勬垚鐨勶紝涓涓渾閿ョ殑搴曢潰鍗婂緞涓篟1锛岄珮涓篽锛屽彟涓涓渾閿ョ殑搴曢潰鍗婂緞涓篟2锛圧2=R1+d锛夛紝楂樹篃涓篽銆傚叾涓璬涓哄渾鍙扮殑涓嬪簳闈㈠崐寰勪笌涓婂簳闈㈠崐寰勪箣宸傚渾鍙扮殑...
绛旓細鍦嗗彴浣撶Н鍏紡锛歏=1/3蟺h锛坮²锛媌aiR²锛媟R锛夈傚洯鍙颁綋浣撶Н閫氳繃V=1/3蟺h锛坮²锛媌aiR²锛媟R锛夎绠銆傝В閲婏細鍦嗗彴鐨勪笂銆佷笅搴曢潰鐨勫崐寰勫垎鍒槸r锛孯锛岄珮鏄痟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〃绀哄渾鍙般俈锛氭槸鎴敟浣撶殑浣撶Н銆傁锛氭槸鏁板甯告暟pi...
绛旓細鍦嗛敟浣撶Н鐨勮绠楀叕寮忔槸锛歏=1/3Sh锛圴=1/3蟺r^2h锛塖鏄簳闈㈢Н锛宧鏄珮锛宺鏄簳闈㈠崐寰勩傚渾鍙版槸鍦嗛敟琚埅鍘讳笂闈㈠皬鍦嗛敟閮ㄥ垎鎵褰㈡垚銆傛晠鑰屽叾浣撶Н鐨勮绠楀叕寮忓疄涓轰袱鍦嗛敟浣撶Н璁＄畻鍏紡鐨勭浉鍑忋傛墍浠ュ叾璁＄畻鍏紡涓猴細V(鍦嗗彴)=V(澶у渾閿)-V(琚埅灏忓渾閿)锛屽強锛歏(鍦嗗彴)=1/3蟺锛圧^2H-r^2h锛夛紝鍏朵腑R涓哄渾鍙板簳闈...
绛旓細鍦嗗彴浣撶Н鍏紡 V=1/3 * 蟺 * h 锛圧^2+Rr+r^2)鍏跺疄鍦嗗彴 鐩稿綋浜 澶у渾閿 鍒囧幓椤剁鐨勫皬鍦嗛敟 銆傚渾閿ヤ綋鐨勪綋绉細 V=1/3 * 蟺 * h * r^2 鍋囪锛屽渾鍙板簳闈㈠崐寰勪负 R 锛岄《闈㈠崐寰勪负 r 锛屽彴楂 h 锛 鍒欏亣璁剧殑澶у渾閿ヤ綋绉 V1=1/3 * 蟺 * h1 * R^2 锛涘皬鍦嗛敟鐨勪綋绉 V2=1/3 * 蟺...
