【人教版】九年级上册数学第二十四章 圆（七）
2022-11-23 15:53:42 11 举报AI智能生成
人教版九年级上册数学第二十四章圆思维导图分享！包含扇形、圆、圆锥、阴影部分面积、圆方程的重要计算公式。通过思维导图系统梳理纷繁琐碎的知识点，用理解力增加记忆力。
作者其他创作
大纲/内容
扇形
弧长：若一条弧所对的圆心角是n<span class="equation-text" data-index="0" data-equation="^\circ" contenteditable="false"><span></span><span></span></span>，半径是R，则弧长 l=<span class="equation-text" data-index="1" data-equation="{nπR \over 180}" contenteditable="false"><span></span><span></span></span><br>
面积：若一条弧所对的圆心角是n<span class="equation-text" data-index="0" data-equation="^\circ" contenteditable="false"><span></span><span></span></span>，半径是 R，则面积 S=<span class="equation-text" data-index="1" data-equation="{nπR^2 \over 360}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="2" data-equation="{1 \over 2}" contenteditable="false"><span></span><span></span></span>lR<br>
圆
周长：C=2兀R
面积：S=兀R<span class="equation-text" data-index="0" data-equation="^2" contenteditable="false"><span></span><span></span></span>
圆锥的侧面积与全面积<br>
圆锥的侧面积<br>
S<span class="equation-text" data-index="0" data-equation="_侧" contenteditable="false"><span></span><span></span></span>=πrl
圆锥的全面积<br>
S<span class="equation-text" data-index="0" data-equation="_全" contenteditable="false"><span></span><span></span></span>=S<span class="equation-text" data-index="1" data-equation="_侧" contenteditable="false"><span></span><span></span></span>+S<span class="equation-text" data-index="2" data-equation="_底" contenteditable="false"><span></span><span></span></span>=πrl+πr<span class="equation-text" data-index="3" data-equation="^2" contenteditable="false"><span></span><span></span></span>
阴影部分面积的计算<br>
规则图形的面积，直接利用对应公式计算
不规则图形的面积，要将图形的面积转化为可求图形的面积的和或差，常用方法有
割补法
拼凑法
等积转化法
平移法
旋转法
圆方程
标准方程：(x-a)<span class="equation-text" data-index="0" data-equation="^2" contenteditable="false"><span></span><span></span></span>+ (y-b)<span class="equation-text" data-index="1" data-equation="^2" contenteditable="false"><span></span><span></span></span>=r<span class="equation-text" data-index="2" data-equation="^2" contenteditable="false"><span></span><span></span></span>，(a,b) 是圆心
一般方程：x<span class="equation-text" data-index="0" data-equation="^2" contenteditable="false"><span></span><span></span></span>+y<span class="equation-text" data-index="1" data-equation="^2" contenteditable="false"><span></span><span></span></span>+Dx+Ey+F=0，D=-2a，E= -2b，F=a2+b2
端点式：已知两点(a<span class="equation-text" data-index="0" data-equation="_1" contenteditable="false"><span></span><span></span></span>,b<span class="equation-text" data-index="1" data-equation="_1" contenteditable="false"><span></span><span></span></span>) (a<span class="equation-text" data-index="2" data-equation="_1" contenteditable="false"><span></span><span></span></span>,b<span class="equation-text" data-index="3" data-equation="_2" contenteditable="false"><span></span><span></span></span>) ，则以这两点为直径的圆的方程： (x-a<span class="equation-text" data-index="4" data-equation="_1" contenteditable="false"><span></span><span></span></span>) (x-a<span class="equation-text" data-index="5" data-equation="_2" contenteditable="false"><span></span><span></span></span>) +(y-b<span class="equation-text" data-index="6" data-equation="_1" contenteditable="false"><span></span><span></span></span>) (y-b<span class="equation-text" data-index="7" data-equation="_2" contenteditable="false"><span></span><span></span></span>) =0<br>
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