圆锥体的表面积怎么求？要求推导和详细说明。 求圆锥表面积的推导过程
\u5706\u9525\u7684\u8868\u9762\u79ef\u5982\u4f55\u63a8\u5bfc\uff1f\u63a8\u5bfc\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u5982\u679c\u7528r\u6765\u8868\u793a\u5e95\u9762\u534a\u5f84\uff0cl\u8868\u793a\u5706\u9525\u7684\u6bcd\u7ebf\uff0cn\u00b0\u8868\u793a\u5706\u9525\u4fa7\u9762\u6247\u5f62\u7684\u5706\u5fc3\u89d2\u7684\u5ea6\u6570\uff0c\u5219\u5e95\u9762\u5468\u957f\u4e3a2\u03c0r,\u6240\u4ee5\u6247\u5f62\u7684\u5f27\u7ebf\u957f\u5ea6\u4e5f\u4e3a2\u03c0r\uff0c\u800c\u5f27\u7ebf\u957f\u5ea6\uff08\u6247\u5f62\u6240\u5360\u5706\u5468\u957f\uff09\u5c31\u7b49\u4e8en\u00b0\uff0f360\u00b0.\u6247\u5f62\u6240\u5360\u5706\u662f\u4ee5\u4ee5\u6bcd\u7ebfl\u4e3a\u534a\u5f84\u7684\uff0c\u6240\u4ee5\u5b83\u7684\u5468\u957f\u4e3a2\u03c0r\uff0c\u5f97\u51fa
n\uff0f360 = 2\u03c0r\uff0f2\u03c0l = r\uff0fl
r\uff0f l\u5c31\u662f\u5f27\u7ebf\u957f\u5ea6\u4e0e\u6247\u5f62\u6240\u5360\u5706\u5468\u957f\u4e4b\u6bd4\uff0c\u4e5f\u5c31\u662f\u6247\u5f62\u4e0e\u6247\u5f62\u6240\u5360\u5706\u7684\u9762\u79ef\u4e4b\u6bd4\u3002\u6240\u4ee5\uff0c\u53ea\u9700\u6c42\u51fa\u6247\u5f62\u6240\u5360\u5706\u7684\u9762\u79ef\u518d\u4e58\u4ee5r\uff0fl\u4fbf\u53ef\u4ee5\u5f97\u51fa\u6247\u5f62\u7684\u9762\u79ef\u3002\u800c\u6247\u5f62\u6240\u5360\u5706\u7684\u9762\u79ef\u4e3a\u03c0l2\uff0c\u5373\u53ef\u5f97\u51fa\uff1a
S\u4fa7 = \u03c0l2\u00d7r\uff0fl
= \u03c0rl
\u5411\u524d\u518d\u63a8\u4e00\u6b65\uff0c\u53c8\u5f97\u51fa\u6247\u5f62\u9762\u79ef\u7684\u8ba1\u7b97\u516c\u5f0f\uff1a
S\u4fa7 =\u03c0rl
=1/2\u00d72\u03c0r\u00d7l
= 1/2\u00d7\u5e95\u9762\u5f27\u7ebf\u957f\u00d7 \u6bcd\u7ebf\u957f
\u7531\u6b64\u63a8\u5bfc\u51fa\u5706\u9525\u4fa7\u9762\u6247\u5f62\u9762\u79ef\u7b49\u4e8e\u03c0rl \uff0c\u7b49\u4e8e3\uff0e14\u4e58\u4ee5\u5e95\u9762\u534a\u5f84\u518d\u4e58\u4ee5\u6bcd\u7ebf\u5373\u53ef\u3002\u5706\u9525\u7684\u8868\u9762\u79ef\u4e3a\u4fa7\u9762\u79ef\u52a0\u5e95\u9762\u79ef\uff0c\u53c8\u4e3a\uff1a
S\u8868 = S\u4fa7\uff0bS\u5e95
=\u03c0rl\uff0b\u03c0r2
=\u03c0rl\uff0b\u03c0r\u00d7r
=\u03c0r(l\uff0br)
\u7531\u6b64\u5f97\u51fa\u5706\u9525\u8868\u9762\u79ef\u8ba1\u7b97\u516c\u5f0f\u3002
\u5706\u9525\u67092\u4e2a\u6570\u636e\uff1a\u9ad8h\u548c\u5e95\u7684\u534a\u5f84r\uff0c\u9525\u4f53\u4fa7\u9762\u7684\u957f\u5ea6\uff08\u53ef\u80fd\u5c31\u53eb\u6bcd\u7ebf\uff09\u548ch\u3001r\u7684\u5173\u7cfb\u7b26\u5408\u52fe\u80a1\u5b9a\u7406\uff0c\u5373\u8fd9\u4e2a\u957f\u5ea6\u8bbe\u4e3aL\uff0c\u5219L=\uff08h²+r²)\u5f00\u5e73\u65b9\u3002\u628a\u5706\u9525\u4fa7\u8868\u9762\u5c55\u5f00\uff0c\u5e94\u8be5\u662f\u4e00\u4e2a\u6247\u5f62\uff0c\u8fd9\u4e2a\u6247\u5f62\u7684\u534a\u5f84\u5c31\u662fL\uff0c\u6247\u5f62\u7684\u5f27\u957f\u5c31\u662f\u5e95\u5706\u7684\u5468\u957f\uff0c\u4e3a\uff1a2\u03a0r\u3002\u4ee5L\u4e3a\u534a\u5f84\u7684\u5927\u5706\u7684\u5468\u957f\u4e3a\uff1a2\u03a0L\u3002
\u9762\u79ef\u4e3a\uff1a\u03a0L²=\u03a0\uff08h²+r²)\u3002\u6247\u5f62\u7684\u5f27\u957f\u6bd4\u5927\u5706\u7684\u5468\u957f\u7b49\u4e8e\u6247\u5f62\u7684\u9762\u79ef\u6bd4\u5927\u5706\u7684\u9762\u79ef\u3002
\u6240\u4ee5\uff1a\u5706\u9525\u7684\u4fa7\u9762\u9762\u79ef=\u6247\u5f62\u7684\u9762\u79ef=\u5927\u5706\u9762\u79ef\u00d7\u6247\u5f62\u7684\u5706\u5f27\u957f\u6bd4\u5927\u5706\u5468\u957f
=\u03a0\uff08h²+r²)\u00d72\u03a0r/2\u03a0L
=\u03a0\uff08h²+r²)\u00d7r/L
\u5706\u9525\u7684\u8868\u9762\u79ef=\u03a0\uff08h²+r²)\u00d7r/L+\u03a0r²
母线长为L
底面周长=2πR
沿着母线将圆锥侧面剪开形成一个扇形，底面周长就是扇形的弧长
所以该扇形的圆心角为：2πL/2πR ×360°=L/360R °
所以扇形面积 也就是圆锥侧面积为：（L/360R）÷360 ×π×L�0�5
圆锥底面积为：πR�0�5
所以表面积为：（L/360R）÷360 ×π×L�0�5+πR�0�5
丽洁 啊，你不会？圆锥体积就是：πr�0�5乘以h乘以三分之一Sh×三分之一
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