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第二十八章　圓
28.5 弧長(zhǎng)和扇形面積的計(jì)算
INCLUDEPICTURE"復(fù)習(xí)回顧.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET
1．把半徑為5 cm的球放在長(zhǎng)方體紙盒內(nèi)，球的一部分露出盒外，其截面如圖所示，若CD＝8 cm，則EF的長(zhǎng)為(　　)
A．8 cm B．7 cm C．5 cm D．4 cm
INCLUDEPICTURE"冊(cè)134.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)134.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)134.tif" \* MERGEFORMATINET (第1題)　　INCLUDEPICTURE"冊(cè)135.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)135.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)135.tif" \* MERGEFORMATINET (第3題)
2．一個(gè)半圓形的半徑是8厘米，它的周長(zhǎng)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．如圖，該扇環(huán)的面積是(π取3.14)(　　)
A．43.96 cm2 B．21.98 cm2 C．10.99 cm2 D．23.98 cm2
INCLUDEPICTURE"預(yù)習(xí)效果檢測(cè).tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果檢測(cè).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果檢測(cè).tif" \* MERGEFORMATINET
1．一條弧和經(jīng)過(guò)這條弧端點(diǎn)的兩條________所組成的圖形叫做扇形．
2．在半徑為R的圓中，1°的圓心角所對(duì)的弧長(zhǎng)為_(kāi)_______，1°的圓心角所對(duì)的扇形面積為_(kāi)_______．
3．在半徑為R的圓中，若設(shè)n°的圓心角所對(duì)的弧長(zhǎng)為l，所對(duì)扇形的面積為S，則l＝________，S＝________．
4．半徑為R，弧長(zhǎng)為l的扇形的面積S＝________．
5．圓錐的頂點(diǎn)與底面圓周上________的連線叫做圓錐的母線．圓錐的頂點(diǎn)與__________之間的線段叫做圓錐的高．
6．[2023哈爾濱期中]若扇形的半徑為2，圓心角為90°，則這個(gè)扇形的面積為_(kāi)_______．
7．在半徑為24的圓中，60°的圓心角所對(duì)的弧長(zhǎng)為_(kāi)_______．
8．用一個(gè)圓心角為120°，半徑為4的扇形作為一個(gè)圓錐的側(cè)面，則這個(gè)圓錐的底面圓半徑為_(kāi)_______．
INCLUDEPICTURE"課堂導(dǎo)學(xué).tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識(shí)點(diǎn)1 弧長(zhǎng)公式
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L1.tif" \* MERGEFORMATINET [2023承德二模]某款鐘表的分針長(zhǎng)度為5 cm，則經(jīng)過(guò)30分鐘分針針尖走過(guò)的路線長(zhǎng)為(　　)
A．5π cm B. cm C. cm D. cm
　　　　　　　　　　　　　　
變式1[2023張家口期末]如圖，在⊙O中，AO＝，∠C＝60°，則的長(zhǎng)度為(　　)
INCLUDEPICTURE"冊(cè)136.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)136.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)136.tif" \* MERGEFORMATINET
A．6π B．9π C．2π D．3π
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知識(shí)點(diǎn)2 扇形的面積公式
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L2.tif" \* MERGEFORMATINET 如圖，在2×2的正方形網(wǎng)格中，格點(diǎn)O是半徑為1的圓的圓心，則圖中兩個(gè)小扇形(陰影部分)的面積之和為_(kāi)_________(結(jié)果保留π)．
INCLUDEPICTURE"冊(cè)137.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)137.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)137.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
變式2[2023西安模擬已知扇形的弧長(zhǎng)是2π，圓心角為120°，則該扇形的面積是________．
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知識(shí)點(diǎn)3 圓錐的側(cè)面積和表面積
INCLUDEPICTURE"L3.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L3.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\L3.tif" \* MERGEFORMATINET [2023邢臺(tái)模擬如圖，沿一條母線將圓錐側(cè)面剪開(kāi)并展平，得到一個(gè)扇形，若圓錐的底面圓的半徑r＝3 cm，扇形的圓心角θ＝120°，則該圓錐的母線長(zhǎng)l為_(kāi)_______cm.
INCLUDEPICTURE"冊(cè)138.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)138.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)138.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
變式3如圖所示，在矩形紙片ABCD中，AD＝6 cm，把它分割成正方形紙片ABFE和矩形紙片EFCD后，分別裁出扇形ABF和半徑最大的圓，恰好能作為一個(gè)圓錐的側(cè)面和底面，則此圓錐的表面積為(　　)
INCLUDEPICTURE"冊(cè)139.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)139.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\冊(cè)139.tif" \* MERGEFORMATINET
A．4π cm2 B．5π cm2 C．6π cm2 D．8π cm2
28.5 弧長(zhǎng)和扇形面積的計(jì)算
INCLUDEPICTURE"復(fù)習(xí)回顧.tif" INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\復(fù)習(xí)回顧.tif" \* MERGEFORMATINET
1．A　2.C　3.C
INCLUDEPICTURE"預(yù)習(xí)效果.tif" INCLUDEPICTURE "預(yù)習(xí)效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\預(yù)習(xí)效果.tif" \* MERGEFORMATINET
1．半徑　2.；　3.；
4.lR　5.任意一點(diǎn)； 底面圓心　6.π　7.8π　8.
INCLUDEPICTURE"課堂導(dǎo)學(xué).tif" INCLUDEPICTURE "課堂導(dǎo)學(xué).tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數(shù)JJ河北（北京）\\課堂導(dǎo)學(xué).tif" \* MERGEFORMATINET
例1　A　 變式1.D　例2　　變式2.3π
例3　9　變式3.B

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