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第二十八章　圆
28.5 弧长和扇形面积的计算
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．把半径为5 cm的球放在长方体纸盒内，球的一部分露出盒外，其截面如图所示，若CD＝8 cm，则EF的长为(　　)
A．8 cm B．7 cm C．5 cm D．4 cm
INCLUDEPICTURE"册134.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册134.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册134.tif" \* MERGEFORMATINET (第1题)　　INCLUDEPICTURE"册135.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册135.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册135.tif" \* MERGEFORMATINET (第3题)
2．一个半圆形的半径是8厘米，它的周长是(π取3.14)(　　)
A．25.12厘米 B．12.56厘米 C．41.12厘米 D．50.24厘米
3．如图，该扇环的面积是(π取3.14)(　　)
A．43.96 cm2 B．21.98 cm2 C．10.99 cm2 D．23.98 cm2
INCLUDEPICTURE"预习效果检测.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET
1．一条弧和经过这条弧端点的两条________所组成的图形叫做扇形．
2．在半径为R的圆中，1°的圆心角所对的弧长为________，1°的圆心角所对的扇形面积为________．
3．在半径为R的圆中，若设n°的圆心角所对的弧长为l，所对扇形的面积为S，则l＝________，S＝________．
4．半径为R，弧长为l的扇形的面积S＝________．
5．圆锥的顶点与底面圆周上________的连线叫做圆锥的母线．圆锥的顶点与__________之间的线段叫做圆锥的高．
6．[2023哈尔滨期中]若扇形的半径为2，圆心角为90°，则这个扇形的面积为________．
7．在半径为24的圆中，60°的圆心角所对的弧长为________．
8．用一个圆心角为120°，半径为4的扇形作为一个圆锥的侧面，则这个圆锥的底面圆半径为________．
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知识点1 弧长公式
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET [2023承德二模]某款钟表的分针长度为5 cm，则经过30分钟分针针尖走过的路线长为(　　)
A．5π cm B. cm C. cm D. cm
　　　　　　　　　　　　　　
变式1[2023张家口期末]如图，在⊙O中，AO＝，∠C＝60°，则的长度为(　　)
INCLUDEPICTURE"册136.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册136.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册136.tif" \* MERGEFORMATINET
A．6π B．9π C．2π D．3π
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知识点2 扇形的面积公式
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET 如图，在2×2的正方形网格中，格点O是半径为1的圆的圆心，则图中两个小扇形(阴影部分)的面积之和为__________(结果保留π)．
INCLUDEPICTURE"册137.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册137.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册137.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
变式2[2023西安模拟已知扇形的弧长是2π，圆心角为120°，则该扇形的面积是________．
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知识点3 圆锥的侧面积和表面积
INCLUDEPICTURE"L3.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L3.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L3.tif" \* MERGEFORMATINET [2023邢台模拟如图，沿一条母线将圆锥侧面剪开并展平，得到一个扇形，若圆锥的底面圆的半径r＝3 cm，扇形的圆心角θ＝120°，则该圆锥的母线长l为________cm.
INCLUDEPICTURE"册138.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册138.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册138.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
变式3如图所示，在矩形纸片ABCD中，AD＝6 cm，把它分割成正方形纸片ABFE和矩形纸片EFCD后，分别裁出扇形ABF和半径最大的圆，恰好能作为一个圆锥的侧面和底面，则此圆锥的表面积为(　　)
INCLUDEPICTURE"册139.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册139.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册139.tif" \* MERGEFORMATINET
A．4π cm2 B．5π cm2 C．6π cm2 D．8π cm2
28.5 弧长和扇形面积的计算
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．A　2.C　3.C
INCLUDEPICTURE"预习效果.tif" INCLUDEPICTURE "预习效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET
1．半径　2.；　3.；
4.lR　5.任意一点； 底面圆心　6.π　7.8π　8.
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "课堂导学.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
例1　A　 变式1.D　例2　　变式2.3π
例3　9　变式3.B

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