已知圆锥的高是4cm,母线5cm,求圆锥侧面展开的弧长和圆心角的度数
高是4cm,母线5cm,根据勾股定理可知底面圆的半径为3厘米,弧长=底面圆的周长,所以弧长=6∏（∏为圆周率）圆锥表面积=1/2弧长×母线=15∏
扇形面积S=n∏R^2/360（R为母线）
圆锥表面积=扇形面积
所以15∏=n∏R^2/360
n=216°
绛旓細鍥炵瓟锛氬叏闈㈢Н=渚ч潰绉+搴曢潰绉 鍏堟眰鍗婂緞宸茬煡姣嶇嚎鍜岄珮姹傚崐寰 R=3 鍏ㄩ潰绉=蟺LR=蟺R骞虫柟=15蟺+9蟺=24蟺 浣撶Н=sh(搴曢潰绉*楂)鎴栬=2蟺rh 浣撶Н=4*9蟺=36蟺
绛旓細瑙ｏ細璁惧簳闈㈠崐寰勪负R锛屽洜涓篟^2+H^=L^2 鍗砇^2+4*4=5*5 鎵浠=3 S=鍏RL=鍏*3*5=15鍏=32.97
绛旓細瑙ｏ細2x3.14x3=18.84 18.84/5=3.768 S渚ч潰绉=3.768/6.28x3.14x5x5= 47.1 S搴曢潰绉=3.14x3x3=28.26 S琛ㄩ潰绉=47.1+28.26=75.36 浜诧紝璇锋偍鐐瑰嚮銆愰噰绾崇瓟妗堛戯紝鎮ㄧ殑閲囩撼鏄垜绛旈鐨勫姩鍔涳紝濡傛灉涓嶆槑鐧斤紝璇疯拷闂紝璋㈣阿銆
绛旓細鈭靛渾閿ョ殑搴曢潰鍗婂緞涓3cm锛楂樹负4cm锛鈭鍦嗛敟鐨勬瘝绾闀夸负5cm锛屸埓鍦嗛敟鐨勪晶闈㈢Н涓合脳3脳5=15蟺cm 2 锛屾晠閫塁锛
绛旓細鍦ㄥ渾閿ョ殑杞存埅闈㈡槸涓涓瓑鑵颁笁瑙掑舰锛屽渾閿ョ殑楂樸佸簳闈㈠崐寰勫拰姣嶇嚎鍛堢洿瑙掍笁瑙掑舰鍏崇郴锛岀鍚堝嬀鑲″畾鐞嗭紝鏍规嵁棰樹腑缁欏嚭鏉′欢銆傚彲璁＄畻鍑鍦嗛敟鐨勯珮涓 4 锛鍐嶆牴鎹渾閿ュ叏闈㈢Н鍏紡璁＄畻 S = =蟺RL+蟺R^2 = =蟺*3*5 + 蟺3²= 24蟺
绛旓細鍦嗛敟鐨勯珮锛氣垰(25-16)=3鍘樼背 鍦嗛敟鐨勪綋绉細(1/3)*3.14*4*4*3=50.24绔嬫柟鍘樼背
绛旓細15蟺锛 璇曢鍒嗘瀽锛氬洜涓哄渾閿ョ殑搴曢潰鍗婂緞鏄3,楂樻槸4,鎵浠鍦嗛敟鐨勬瘝绾闀夸负5,鎵浠ヨ繖涓渾閿ョ殑渚ч潰灞曞紑鍥剧殑闈㈢Н鏄脳3脳5=15蟺锛庢晠绛旀鏄15蟺锛
绛旓細鍦嗛敟鐨勯珮锛氣垰(25-16)=3鍘樼背 鍦嗛敟鐨勪綋绉細(1/3)*3.14*4*4*3=50.24绔嬫柟鍘樼背
绛旓細鍦嗛敟搴曢潰鍗婂緞r,楂榟鍜姣嶇嚎L鏋勬垚鐩磋涓夎褰 鍦嗛敟搴曢潰鍗婂緞r=3cm,楂榟=4cm,鈭存瘝绾縇=鈭(3^2+4^2)=5cm 渚ч潰灞曞紑鎵囧舰寮ч暱=搴曢潰鍦嗗懆闀=2蟺*3=6蟺(cm),渚ч潰灞曞紑鎵囧舰鍗婂緞R=姣嶇嚎L=5cm 鈭翠晶闈㈠睍寮鎵囧舰鐨勫渾蹇冭胃=(6蟺/5)*(180掳/蟺)=216掳 ...
绛旓細20蟺 鍒嗘瀽锛氬埄鐢ㄥ嬀鑲″畾鐞嗗彲寰楀渾閿ョ殑搴曢潰鍗婂緞锛岄偅涔堝渾閿ョ殑渚ч潰绉=蟺脳搴曢潰鍗婂緞脳姣嶇嚎闀匡紝鎶婄浉搴旀暟鍊间唬鍏ュ嵆鍙眰瑙ｏ紟瑙ｏ細鈭鍦嗛敟鐨勯珮鏄3cm锛屾瘝绾闀挎槸5cm锛屸埓鍦嗛敟鐨勫簳闈㈠崐寰涓4cm锛鈭村渾閿ョ殑渚ч潰绉=蟺脳4脳5=20蟺cm 2 锛庣偣璇勶細鏈鑰冩煡鍦嗛敟渚ч潰绉殑姹傛硶锛庢敞鎰忓渾閿ョ殑楂橈紝姣嶇嚎闀匡紝搴曢潰鍗婂緞缁勬垚鐩磋...
