用半径为3厘米,圆心角120度的扇形围成一个圆锥的侧面,则这个圆锥的底面半径为 厘米? 用半径为3厘米,圆心是120度的扇形围成一个圆锥的侧面,求圆...
\u7528\u534a\u5f84\u4e3a3cm\uff0c\u5706\u5fc3\u89d2\u662f120\u00b0\u7684\u6247\u5f62\u56f4\u6210\u4e00\u4e2a\u5706\u9525\u7684\u4fa7\u9762\uff0c\u5219\u8fd9\u4e2a\u5706\u9525\u7684\u5e95\u9762\u534a\u5f84\u4e3a\uff08\u3000\u3000\uff09A\uff0e2\u03c0cmB\uff0e1.5cm\u8bbe\u6b64\u5706\u9525\u7684\u5e95\u9762\u534a\u5f84\u4e3ar\uff0c\u6839\u636e\u5706\u9525\u7684\u4fa7\u9762\u5c55\u5f00\u56fe\u6247\u5f62\u7684\u5f27\u957f\u7b49\u4e8e\u5706\u9525\u5e95\u9762\u5468\u957f\u53ef\u5f97\uff0c2\u03c0r=120\u03c0\u00d73180\uff0c\u89e3\u5f97\uff1ar=1cm\uff0e\u6545\u9009D\uff0e
\u5706\u9525\u5e95\u9762\u7684\u5468\u957f\u4e3a:3*3.14*120/180=2*3.14=6.28
\u5706\u9525\u5e95\u9762\u7684\u534a\u5f84\u4e3a:6.28/2*3.14=1 CM
由题意可得圆锥底面圆周长,即扇形弧长为:L=n/180·πr =(120/180)*π*3=2π,所以这个圆锥的底面半径为:2π/2π=1.
圆锥底面的周长为:3*3.14*120/180=2*3.14=6.28
圆锥底面的半径为:6.28/2*3.14=1 CM
绛旓細涓涓渾褰㈢殑鍗婂緞鏄3鍘樼背锛鎵囧舰鐨鍦嗗績瑙鏄120掳锛岃繖涓墖褰㈢殑鍛ㄩ暱鏄紙12銆28锛夊帢绫筹紝闈㈢Н鏄紙9銆42锛夊钩鏂瑰帢绫炽傚渾鐨勫懆闀挎槸锛2*3銆14*3=18銆84鍘樼背 鎵囧舰鐨勫懆闀=1/3鍦嗗懆闀+2鍗婂緞=1/3*18銆84+2*3=12銆28 闈㈢Н鏄細1/3*3銆14*3*3=9銆42 ...
绛旓細鎵囧舰闈㈢НS =[锛鍦嗗績瑙鐨勫害鏁帮級梅锛360锛塢脳3.14*R鐨勫钩鏂 =(120梅360锛壝3.14脳3脳3 =9.42(骞虫柟鍘樼背)
绛旓細鍒嗘瀽锛氭墖褰㈢殑鍦嗗績瑙掓槸120搴锛岃鏄庡畠鐨勯潰绉槸浠3鍘樼背涓鍗婂緞鐨勫渾鐨勯潰绉殑120搴/360搴︼紝鍗1/3.鍙姹傚嚭鍦嗙殑闈㈢Н鍐嶄箻浠1/3灏卞彲浠ヤ簡 3.14*3*3*1/3=9.42骞虫柟鍘樼背 绛旓細瀹冪殑闈㈢Н鏄9.42骞虫柟鍘樼背 銆
绛旓細鍦ㄤ竴涓鍗婂緞涓3cm鐨勫渾涓,鐢讳竴涓鍦嗗績瑙涓120搴鐨勬墖褰,杩欎釜鎵囧舰鐨勯潰绉=1/3脳鍦嗙殑闈㈢Н =1/3脳3.14脳3脳3 =9.42骞虫柟鍘樼背锛
绛旓細鍥犱负(鍏*3*3)*120/360 =9鍏*1/3 =3鍏 =3*3.14 =9.42(骞虫柟鍘樼背)鎵浠ワ紝鎵囧舰闈㈢Н鏄9.42骞虫柟鍘樼背銆
绛旓細L=120脳3脳3.14/180 =2脳3.14
绛旓細120掳脳蟺脳3 l=---=2蟺锛鍘樼背锛夆増6.28锛堝帢绫筹級180掳
绛旓細搴曢潰鍦嗗懆闀匡細2*3蟺*240/360=4蟺 鍦伴潰鍦嗗崐寰勶細4蟺/2蟺=2cm 鎵浠ヨ繖涓渾閿ュ簳闈㈠渾鐨鍗婂緞涓2cm銆
绛旓細3脳2脳3.14梅360脳120+3+3=12.28鍘樼背
绛旓細璁 n鏄搴︼紝S鏄墖褰㈤潰绉紝r鏄墖褰㈢殑鍗婂緞锛S=n*蟺*r*r/360 鎵浠ヨ繖閬撻绛変簬 S=120*蟺*3*3/360 =3蟺