已知圆锥的底面半径为,母线长为,则此圆锥的侧面积为 已知圆锥的底面半径为1cm，母线长为1cm，则它的侧面积是_...
1.\u5df2\u77e5\u5706\u9525\u7684\u5e95\u9762\u534a\u5f84\u4e3a2\uff0c\u6bcd\u7ebf\u957f\u4e3a5\uff0c\u5219\u5706\u9525\u7684\u4fa7\u9762\u79ef\u4e3a_,\u82e5\u5706\u9525\u7684\u9525\u89d2\u4e3a90\u00b0\uff0c\u6bcd\u7ebf\u957f\u4e3a4\uff0c\u5219\u5706\u9525\u7684\u5168\u9762\u79ef1
\u4fa7\u9762\u5c55\u5f00\u4e3a\u6247\u5f62\uff0c\u6247\u5f62\u534a\u5f84=\u6bcd\u7ebf\u957f=5\uff0c\u5f27\u957f=\u5e95\u9762\u5468\u957f=2*2*\u03c0=4\u03c0\uff0c
\u4fa7\u9762\u79ef=\u6247\u5f62\u9762\u79ef=\u534a\u5f84x\u5f27\u957f/2=5x4\u03c0/2=10\u03c0\uff1b
\u82e5\u5706\u9525\u7684\u9525\u89d2\u4e3a90\u00b0\uff0c\u6bcd\u7ebf\u957f\u4e3a4\uff0c\u5219\u5706\u9525\u5e95\u9762\u76f4\u5f84²=4²+4²=32\uff1b
\u5e95\u9762\u76f4\u5f84=4\u221a2\uff0c\u5e95\u9762\u534a\u5f84=2\u221a2\uff0c\u5e95\u9762\u5468\u957f=4\u03c0\u221a2\uff0c
\u5168\u9762\u79ef=\u5e95\u9762\u79ef+\u4fa7\u9762\u79ef
=\u03c0\uff082\u221a2\uff09²+4\u03c0\u221a2*4/2
=8\u03c0(1+\u221a2)
2
\u8bbe\u5927\u5706\u534a\u5f84R=10,
\u5c0f\u5706\u534a\u5f84r=12\u03c0/(2\u03c0)=6
r:R=AD:AC
6\uff1a10=AD:(AD+DC)
10AD=6*(AD+24)
4AD=6*24
AD=36
AC=AD+DC=36+24=60
\u622a\u9762\u4ee5\u4e0b\u7684\u51e0\u4f55\u4f53\u7684\u4fa7\u9762\u79ef=\u534a\u5f84\u4e3a60\uff0c\u5f27\u957f\u4e3a20\u03c0\u7684\u6247\u5f62\u9762\u79ef-\u534a\u5f84\u4e3a36\uff0c\u5f27\u957f\u4e3a12\u03c0\u7684\u6247\u5f62\u9762\u79ef
=60x20\u03c0/2-36x12\u03c0/2
=600\u03c0-216\u03c0
=384\u03c0
\u2235\u5706\u9525\u7684\u5e95\u9762\u534a\u5f84\u4e3a1cm\uff0c\u2234\u5706\u9525\u7684\u5e95\u9762\u5468\u957f\u4e3a\uff1a2\u03c0r=2\u03c0cm\uff0c\u2235\u5706\u9525\u7684\u4fa7\u9762\u5c55\u5f00\u6247\u5f62\u7684\u5f27\u957f\u7b49\u4e8e\u5706\u9525\u7684\u5468\u957f\uff0c\u2234\u5706\u9525\u7684\u4fa7\u9762\u79ef\u4e3a\uff1a12lr=12\u00d72\u03c0\u00d71=\u03c0cm2\uff0c\u6545\u7b54\u6848\u4e3a\uff1a\u03c0\uff0e
利用圆锥的底面半径为,母线长为,直接利用圆锥的侧面积公式求出即可.解:依题意知母线长,底面半径,
则由圆锥的侧面积公式得.
故答案为:.
此题主要考查了圆锥侧面面积的计算,熟练记忆圆锥的侧面积公式是解决问题的关键.
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绛旓細瑙;璁惧皬鍦嗛敟鐨勫崐寰勪负r锛屾瘝绾块暱涓n,鐢遍鎰忕煡锛歋澶у渾閿=1/2*2蟺R*2R S灏忓渾閿=1/2*2蟺r*n 鍥犱负r/R=n/(2R)鎵浠灏忓渾閿/S澶у渾閿=1/2*2蟺r*n/[1/2*2蟺R*2R]=(r/R)^2=1/2 鎵浠=(鈭2/2)R
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