如果一个圆锥的正视图顶角为40°,那么它的侧面展开图的度数为多少? 详细点
\u82e5\u4e00\u4e2a\u5706\u9525\u7684\u5e95\u9762\u79ef\u662f\u4fa7\u9762\u79ef\u7684\u4e09\u5206\u4e4b\u4e00\uff0c\u5219\u8be5\u5706\u9525\u4fa7\u9762\u5c55\u5f00\u56fe\u7684\u5706\u5f62\u89d2\u7684\u5ea6\u6570\u662f\u591a\u5c11\u5ea6\u5e95\u9762\u79ef\u4e3a \u03c0 r²\uff0c \u4fa7\u9762\u79ef\u4e3a \u03c0 r l\uff0c
\u4f9d\u9898\u610f\u5f97 \u03c0 r²\uff1a\u03c0 r l=1:3\u5373\u5e95\u9762\u534a\u5f84\u4e0e\u6bcd\u7ebf\u4e4b\u6bd4\u4e3a r\uff1al=1:3
\u4fa7\u9762\u5c55\u5f00\u6247\u5f62\u7684\u5706\u5fc3\u89d2\u4e3a\u5e95\u9762\u5468\u957f\u5360\u4fa7\u9762\u5c55\u5f00\u5706\u7684\u5468\u957f\u7684\u6bd4\u4f8b\u4e58\u4ee5360\u00b0\uff1a
\uff082\u03c0r/2\u03c0l\uff09\u00d7360\u00b0=\uff081/3\uff09\u00d7360\u00b0=120\u00b0
\u9700\u8981\u7528\u5230\u7684\u516c\u5f0f\u6709
\u6247\u5f62\u9762\u79ef\uff1aS=n\u03c0a^2/360
\u5706\u9762\u79ef\uff1aS=\u03c0r^2
\u5706\u9525\u4fa7\u9762\u79ef\uff1aS=\u03c0ra\uff08n\u4e3a\u5706\u5fc3\u89d2,a\u4e3a\u6bcd\u7ebf\uff09
\u8fc7\u7a0b
\u89e3\uff1a\u56e0\u4e3a\u5706\u9525\u4fa7\u9762\u79ef=\u5e95\u9762\u5706\u9762\u79ef\u76842\u500d
\u6240\u4ee5\u03c0ra=2\u03c0r^2
a=2r
\u53c8\u56e0\u4e3a\u5706\u9525\u4fa7\u9762\u5c55\u5f00\u7684\u6247\u5f62\u9762\u79ef=\u5e95\u9762\u5706\u9762\u79ef\u76842\u500d
\u6240\u4ee5n\u03c0a^2/360=2\u03c0r^2
\u5373n\u03c0\uff082r)^2/360=2\u03c0r^2
4n\u03c0r^2/360=2\u03c0r^2
n=2\u03c0r^2/(4\u03c0r^2/360)
n=180
\u6240\u4ee5\u8fd9\u4e2a\u5706\u9525\u4fa7\u9762\u5c55\u5f00\u56fe\u7684\u5706\u5fc3\u89d2\u5ea6\u6570\u4e3a180\u5ea6\u3002
n=r/l*360
则n=360*sin20°
j即圆心角的度数(360sin20°)°
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