圆的弧长和图形面积的计算
一、选择题(每小题6分，共24分)
1．(2014·襄阳)用一个圆心角为120°，半径为3的扇形作一个圆锥的侧面，则这个圆锥的底面半径为( B )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=7&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"7","h":"36","dataType":"gif","c":"word/media/image1.png"})
B．1 C. D．2
![](https://wkrtcs.bdimg.com/rtcs/image?w=81&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"81","h":"82","dataType":"png","c":"word/media/image3.png","imgOriW":509,"imgOriH":520})
2．(2013·河北)如图，AB是⊙O的直径，弦CD⊥AB，∠C＝30°，CD＝2![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"13","h":"16","dataType":"gif","c":"word/media/image4.png"})
，则S阴影＝( D )
A．π B．2π
C. ![](https://wkrtcs.bdimg.com/rtcs/image?w=7&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"7","h":"37","dataType":"gif","c":"word/media/image5.png"})
D.π
3．(2014·金华)一张圆心角为45°的扇形纸板和一张圆形纸板按如图方式分别剪成一个正方形，边长都为1，则扇形和圆形纸板的面积比是( A )
![](https://wkrtcs.bdimg.com/rtcs/image?w=141&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"141","h":"60","dataType":"png","c":"word/media/image6.png","imgOriW":880,"imgOriH":378})
A．5∶4 B．5∶2
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=13&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"13","h":"16","dataType":"gif","c":"word/media/image7.png"})
∶2 D.∶
![](https://wkrtcs.bdimg.com/rtcs/image?w=74&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"74","h":"70","dataType":"png","c":"word/media/image9.png","imgOriW":470,"imgOriH":440})
4．(2014·东营)如图，已知扇形的圆心角为60°，半径为，则图中弓形的面积为( C )
A.![](https://wkrtcs.bdimg.com/rtcs/image?w=55&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"55","h":"35","dataType":"gif","c":"word/media/image10.png"})
B.
C.![](https://wkrtcs.bdimg.com/rtcs/image?w=55&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"55","h":"35","dataType":"gif","c":"word/media/image12.png"})
D.
二、填空题(每小题7分，共28分)
5．(2014·泰州)圆锥的底面半径为6 cm，母线长为10 cm，则圆锥的侧面积为__60π__cm2.
6．(2013·重庆)如图，一个圆心角为90°的扇形，半径OA＝2，那么图中阴影部分的面积为__π－2__．(结果保留π)．
![](https://wkrtcs.bdimg.com/rtcs/image?w=102&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"102","h":"70","dataType":"png","c":"word/media/image14.png","imgOriW":635,"imgOriH":440})
,第6题图) ,第7题图)
7．(2013·泸州)如图，从半径为9 cm的圆形纸片上剪去![](https://wkrtcs.bdimg.com/rtcs/image?w=7&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"7","h":"37","dataType":"gif","c":"word/media/image16.png"})
圆周的一个扇形，将留下的扇形围成一个圆锥(接缝处不重叠)，那么这个圆锥的高为__3__ cm.
解析：圆心角是360×(1－![](https://wkrtcs.bdimg.com/rtcs/image?w=8&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"8","h":"37","dataType":"gif","c":"word/media/image18.png"})
)＝240°，则弧长是＝12π(cm)．设圆锥的底面半径是r，则2πr＝12π，解得r＝6，则圆锥的高是＝3 (cm)
![](https://wkrtcs.bdimg.com/rtcs/image?w=89&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"89","h":"79","dataType":"png","c":"word/media/image22.png","imgOriW":554,"imgOriH":501})
8．(2013·昆明)如图，从直径为4 cm的圆形纸片中，剪出一个圆心角为90°的扇形OAB，且点O，A，B在圆周上，把它围成一个圆锥，则圆锥的底面圆的半径是__![](https://wkrtcs.bdimg.com/rtcs/image?w=17&md5sum=61b6aeeb9762de0f29f283e47311d595&sign=200af2b003&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=51&ipr={"t":"img","w":"17","h":"37","dataType":"gif","c":"word/media/image23.png"})
__cm.
三、解答题(共48分)
9．(12分)(2013·新疆)如图，已知⊙O的半径为4，CD是⊙O的直径，AC为⊙O的弦，B为CD延长线上的一点，∠ABC＝30°，且AB＝AC.
(1)求证：AB为⊙O的切线；
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