锟斤拷锟斤拷1.锟斤拷锟叫學(xu锟斤拷)锟揭傦拷只锟斤拷直锟紸锟斤拷锟斤拷直锟紸锟紽锟斤拷直锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷锟皆岋拷(du锟斤拷)锟紸锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷锟紻(zhu锟斤拷n)锟斤拷锟絰锟斤拷锟斤拷(sh锟斤拷)锟紿锟斤拷锟斤拷直锟紸锟斤拷锟斤拷直锟紸锟紽锟斤拷直锟紸锟絖(t锟斤拷i)锟侥讹拷锟絰锟斤拷

锟斤拷锟斤拷锟紷锟接讹拷锟絰直锟絕锟斤拷锟襟，憋拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟揭岋拷(du锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷锟絴(zh锟斤拷)也锟斤拷锟狡岋拷(d锟斤拷o)锟斤拷

锟斤拷锟斤拷锟斤拷(du锟斤拷)锟斤拷锟斤拷亩锟斤拷x锟斤拷锟斤拷要注锟斤拷^(q锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷锟侥革拷锟筋，锟斤拷锟角岋拷(sh锟斤拷)锟侥碉拷锟斤拷

锟斤拷锟斤拷锟斤拷邊锟紸锟斤拷锟酵碉拷邊锟紸锟紽锟斤拷锟斤拷锟斤拷A锟斤拷锟酵圓锟紽锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絊锟斤拷锟斤拷锟�(l锟斤拷i)锟斤拷锟絰锟斤拷锟斤拷锟节岋拷(sh锟斤拷)锟絗锟斤拷锟絓(y锟斤拷n)锟斤拷锟絕锟絍锟斤拷要注锟斤拷锟絚一锟斤拷A锟斤拷锟斤拷锟紸锟紽锟侥區(q锟斤拷)锟斤拷锟斤拷

锟斤拷锟斤拷2.锟紸锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟斤拷锟斤拷锟斤拷锟斤拷|(zh锟斤拷)

锟斤拷锟斤拷(1)锟紸锟斤拷锟斤拷锟斤拷锟絴(zh锟斤拷)锟斤拷要锟斤拷(qi锟斤拷ng)锟絳(di锟斤拷o)锟斤拷锟絚(di锟斤拷n)锟斤拷一锟斤拷锟紹锟侥撅拷(xi锟斤拷n)锟斤拷直锟紸锟斤拷锟侥碉拷锟斤拷;锟斤拷锟斤拷锟斤拷锟斤拷(g锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷|(zh锟斤拷)——平锟斤拷锟节碉拷锟斤拷慕锟斤拷锟斤拷锟斤拷c锟斤拷锟斤拷全锟饺的圓;锟絊锟斤拷锟斤拷锟斤拷一锟斤拷(g锟斤拷)锟斤拷锟较★拷锟铰碉拷锟斤拷A锟斤拷直锟斤拷锟斤拷母锟斤拷(xi锟斤拷n)锟斤拷锟組锟缴的撅拷锟斤拷;平锟斤拷锟斤拷锟絊锟斤拷(xi锟斤拷n)锟侥斤拷锟斤拷锟斤拷一锟斤拷(g锟斤拷)锟斤拷锟斤拷锟斤拷锟铰底的圓锟斤拷锟揭猴拷母锟斤拷(xi锟斤拷n)锟組锟缴的撅拷锟斤拷锟斤拷

锟斤拷锟斤拷(2)锟紸锟紽锟斤拷锟斤拷锟絴(zh锟斤拷)锟斤拷要锟斤拷(qi锟斤拷ng)锟絳(di锟斤拷o)锟斤拷锟絚(di锟斤拷n)

锟斤拷锟斤拷锟斤拷平锟斤拷锟节碉拷锟斤拷慕锟斤拷锟紸锟斤拷锟斤拷锟絴(zh锟斤拷)锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷A锟斤拷e锟酵碉拷锟斤拷A锟斤拷e锟侥比碉拷锟节忥拷锟斤拷c(di锟斤拷n)锟斤拷锟斤拷锟斤拷蛷锟斤拷锟絚(di锟斤拷n)锟斤拷锟斤拷锟斤拷锟斤拷x锟斤拷平锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟絕(gu锟斤拷)锟紸锟紽锟斤拷锟斤拷c(di锟斤拷n)锟斤拷锟斤拷锟絚锟斤拷锟斤拷锟斤拷嘟伙拷慕锟斤拷锟斤拷锟揭伙拷锟�(g锟斤拷)锟缴兩條母锟斤拷(xi锟斤拷n)锟酵碉拷锟斤拷A锟斤拷锟揭組锟缴的碉拷锟斤拷锟斤拷锟斤拷锟轿ｏ拷锟斤拷锟斤拷e锟介：

锟斤拷锟斤拷锟斤拷知锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟轿碉拷頂角诧拷锟斤拷锟斤拷锟絊锟斤拷锟斤拷锟巾斀锟�(锟斤拷D10-20)锟斤拷锟铰岋拷(sh锟斤拷)锟斤拷锟斤拷锟斤拷BC≥AB锟斤拷VC=VB=VA锟缴碉拷∠AVB≤BVC.

锟斤拷锟斤拷锟斤拷锟节斤拷锟斤拷锟斤拷锟斤拷锟轿碉拷頂角诧拷锟斤拷锟斤拷锟絊锟斤拷锟斤拷锟巾斀锟�锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷(d锟斤拷ng)锟絊锟斤拷锟斤拷锟巾斀锟�θ≤90°锟斤拷锟斤拷0°<α≤θ≤90°锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷(d锟斤拷ng)锟絊锟斤拷锟斤拷锟巾斀锟�θ>90°锟絩(sh锟斤拷)锟斤拷锟絊锟斤拷锟斤拷锟斤拷锟絜锟絪锟斤拷锟斤拷锟斤拷锟侥ｏ拷锟紷锟斤拷锟斤拷?y锟斤拷n)锟�锟斤拷锟�?0°≤α<θ<180°锟絩(sh锟斤拷)锟斤拷1≥sinα>sinθ>0.

锟斤拷锟�锟斤拷蹐A锟紽锟斤拷母锟斤拷(xi锟斤拷n)l锟斤拷锟斤拷h(yu锟斤拷n)锟酵碉拷锟斤拷A锟侥半徑锟組锟斤拷一锟斤拷(g锟斤拷)直锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟紸锟紽锟斤拷锟斤拷锟絇(gu锟斤拷n)計(j锟斤拷)锟姐問(w锟斤拷n)锟絵锟斤拷一锟姐都要?d锟斤拷)w锟結(ji锟斤拷)锟斤拷锟斤拷@锟斤拷(g锟斤拷)直锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟截別锟斤拷锟絇(gu锟斤拷n)系式

锟斤拷锟斤拷l2=h2+R2

锟斤拷锟斤拷(3)锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷锟絴(zh锟斤拷)锟斤拷锟斤拷锟角忥拷“锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷^锟紸锟紽”锟紷锟斤拷(g锟斤拷)锟铰岋拷(sh锟斤拷)锟狡得碉拷锟斤拷锟斤拷锟斤拷要锟斤拷(qi锟斤拷ng)锟絳(di锟斤拷o)锟斤拷锟斤拷锟斤拷c(di锟斤拷n)锟斤拷

锟斤拷锟斤拷锟劫圓锟絖(t锟斤拷i)锟斤拷母锟斤拷(xi锟斤拷n)锟斤拷锟絚(di锟斤拷n)锟斤拷锟斤拷锟斤拷锟轿兩條母锟斤拷(xi锟斤拷n)锟絖锟斤拷锟侥斤拷锟斤拷锟揭伙拷锟斤拷锟斤拷锟斤拷锟�锟斤拷锟斤拷锟角ｏ拷锟絚锟斤拷锟斤拷锟铰碉拷锟芥都锟洁交锟侥斤拷锟芥不一锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷一锟斤拷锟角碉拷锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟�锟斤拷锟狡斤拷锟斤拷诘锟斤拷锟侥斤拷锟斤拷锟紧將圓锟絖(t锟斤拷i)锟侥高分成撅拷锟斤拷锟斤拷锟铰兩底烇拷啥蔚慕锟斤拷锟斤拷锟絜锟斤拷S锟斤拷锟絫

锟斤拷锟斤拷锟斤拷锟斤拷S1锟斤拷S2锟街別锟斤拷锟斤拷锟斤拷锟铰碉拷锟斤拷锟斤拷e锟斤拷

锟斤拷锟斤拷锟侥斤拷锟斤拷锟斤拷锟絴(zh锟斤拷)锟斤拷锟狡廣锟斤拷

锟斤拷锟�锟斤拷蹐A锟絖(t锟斤拷i)锟斤拷母锟斤拷(xi锟斤拷n)l锟斤拷锟斤拷h(yu锟斤拷n)锟斤拷锟斤拷锟斤拷锟铰兩底圓锟侥半徑r锟斤拷R锟斤拷锟組锟斤拷一锟斤拷(g锟斤拷)直锟斤拷锟斤拷锟轿ｏ拷锟斤拷锟斤拷

锟斤拷锟斤拷l2=h2+(R-r)2

锟斤拷锟斤拷锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷锟絇(gu锟斤拷n)計(j锟斤拷)锟姐問(w锟斤拷n)锟絵锟斤拷锟斤拷锟絯锟結(ji锟斤拷)锟斤拷锟斤拷@锟斤拷(g锟斤拷)直锟斤拷锟斤拷锟轿★拷

锟斤拷锟斤拷(4)锟斤拷锟斤拷锟斤拷|(zh锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絴(zh锟斤拷)锟斤拷

锟斤拷锟�锟斤拷锟斤拷锟斤拷锟斤拷锟狡斤拷锟斤拷锟斤拷锟斤拷锟矫的斤拷锟斤拷锟斤拷一锟斤拷(g锟斤拷)锟紸锟斤拷锟斤拷锟斤拷锟侥和斤拷锟斤拷A锟紸锟侥碉拷锟紹锟斤拷(xi锟斤拷n)锟絚锟紷锟斤拷(g锟斤拷)锟斤拷锟芥垂直锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絉锟斤拷r锟街別锟斤拷示锟斤拷陌霃斤拷徒锟斤拷锟紸锟侥半徑锟斤拷d锟斤拷示锟斤拷锟侥碉拷锟斤拷锟斤拷木锟斤拷x锟斤拷锟絫

锟斤拷锟斤拷R2=r2+d2

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷陌霃�锟斤拷锟斤拷锟斤拷A锟侥半徑锟斤拷锟斤拷锟斤拷锟侥碉拷锟斤拷锟斤拷木锟斤拷x锟組锟斤拷一锟斤拷(g锟斤拷)直锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絇(gu锟斤拷n)锟斤拷锟接�(j锟斤拷)锟姐問(w锟斤拷n)锟絵锟斤拷锟斤拷锟絯锟結(ji锟斤拷)锟斤拷锟斤拷@锟斤拷(g锟斤拷)直锟斤拷锟斤拷锟斤拷锟轿★拷3.锟紸锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷谋锟斤拷锟絜

锟斤拷锟斤拷(1)锟紸锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟絖(t锟斤拷i)锟酵讹拷锟斤拷锟絯一锟接讹拷锟角匡拷锟斤拷平锟斤拷展锟絖(k锟斤拷i)锟斤拷锟斤拷

锟斤拷锟�锟斤拷賵A锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟絖(t锟斤拷i)锟侥傦拷(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟斤拷锟斤拷锟斤拷锟斤拷锟�(c锟斤拷)锟斤拷e锟侥伙拷锟斤拷锟斤拷锟斤拷(j锟斤拷)锟斤拷

锟斤拷锟斤拷锟紸锟斤拷锟侥傦拷(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟斤拷锟斤拷锟缴碉拷锟斤拷D锟斤拷锟斤拷锟絃(zh锟斤拷ng)锟斤拷母锟斤拷(xi锟斤拷n)锟絃(zh锟斤拷ng)锟組锟缴碉拷一锟斤拷(g锟斤拷)锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷锟节圓锟紽锟酵傦拷(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟斤拷一锟斤拷(g锟斤拷)锟缴兩條母锟斤拷(xi锟斤拷n)锟絃(zh锟斤拷ng)锟酵碉拷锟斤拷A锟斤拷锟斤拷锟絃(zh锟斤拷ng)锟組锟缴碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟轿的圓锟侥角烇拷

锟斤拷锟斤拷锟桔圓锟絖(t锟斤拷i)锟侥傦拷(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟斤拷一锟斤拷(g锟斤拷)锟缴兩條母锟斤拷(xi锟斤拷n)锟絃(zh锟斤拷ng)锟斤拷锟斤拷锟斤拷锟铰碉拷锟斤拷锟斤拷锟絃(zh锟斤拷ng)锟組锟缴碉拷锟饺環(hu锟斤拷n)锟斤拷锟斤拷锟饺環(hu锟斤拷n)锟侥圓锟侥角烇拷

锟斤拷锟斤拷锟紷锟斤拷(g锟斤拷)锟斤拷式锟斤拷锟斤拷锟节匡拷锟絞锟阶猴拷锟絯锟斤拷锟斤拷锟�(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟侥伙拷锟斤拷

锟斤拷锟斤拷锟紷然锟斤拷锟斤拷(d锟斤拷ng)r=0锟絩(sh锟斤拷)锟斤拷锟紷锟斤拷(g锟斤拷)锟斤拷式锟斤拷锟角圓锟紽锟斤拷(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟斤拷锟轿的圓锟侥角癸拷式锟斤拷锟斤拷锟皆ｏ拷锟紸锟紽锟斤拷(c锟斤拷)锟斤拷展锟絖(k锟斤拷i)锟紻锟斤拷锟轿的圓锟侥角癸拷式锟角圓锟絖(t锟斤拷i)锟斤拷锟絇(gu锟斤拷n)锟角碉拷锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷(2)锟紸锟斤拷锟斤拷锟紸锟紽锟酵圓锟絖(t锟斤拷i)锟侥傦拷(c锟斤拷)锟芥公式锟斤拷

锟斤拷锟斤拷S锟斤拷(c锟斤拷)=π(r+R)l

锟斤拷锟斤拷锟斤拷(d锟斤拷ng)r=R锟絩(sh锟斤拷)锟斤拷S锟斤拷(c锟斤拷)=2πRl锟斤拷锟斤拷锟紸锟斤拷锟侥傦拷(c锟斤拷)锟斤拷e锟斤拷式锟斤拷

锟斤拷锟斤拷锟斤拷(d锟斤拷ng)r=0锟絩(sh锟斤拷)锟斤拷S锟斤拷(c锟斤拷)=rRl锟斤拷锟斤拷锟紸锟紽锟斤拷锟斤拷e锟斤拷式锟斤拷

锟斤拷锟斤拷要锟斤拷視锟斤拷锟斤拷(c锟斤拷)锟斤拷e锟絞锟斤拷锟紷锟絅锟絇(gu锟斤拷n)系锟斤拷

锟斤拷锟斤拷(3)锟斤拷锟斤拷锟角诧拷锟斤拷平锟斤拷展锟絖(k锟斤拷i)锟侥圖锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷e锟侥凤拷锟斤拷锟絚锟斤拷锟斤拷锟紽锟斤拷锟絖(t锟斤拷i)锟侥凤拷锟斤拷锟斤拷全锟斤拷同锟斤拷

锟斤拷锟斤拷锟狡岋拷(d锟斤拷o)锟斤拷锟斤拷(l锟斤拷i)锟斤拷要锟斤拷“微锟絜锟斤拷”锟饺高等旓拷(sh锟斤拷)锟絎(xu锟斤拷)锟斤拷知锟絉(sh锟斤拷)锟斤拷锟絥锟斤拷锟较诧拷锟斤拷锟斤拷锟斤拷一锟絅锟紺锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷規(gu锟斤拷)锟絫锟紸锟轿的讹拷锟斤拷锟斤拷锟皆的筹拷锟矫凤拷锟斤拷锟斤拷“锟斤拷(x锟斤拷)锟斤拷——锟斤拷锟�——取锟絆锟斤拷”锟斤拷锟紷锟絅锟斤拷锟斤拷锟斤拷锟节學(xu锟斤拷)锟斤拷“微锟絜锟斤拷”锟斤拷锟斤拷锟絇(gu锟斤拷n)锟斤拷(n锟斤拷i)锟捷后，诧拷锟紺锟斤拷锟斤拷锟斤拷锟紷锟斤拷锟斤拷浴锟�

锟斤拷锟斤拷4.锟斤拷(hu锟斤拷)锟紸锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟絖(t锟斤拷i)锟斤拷锟斤拷锟街憋拷^锟紻锟侥凤拷锟斤拷——锟斤拷锟饺測(c锟斤拷)

锟斤拷锟斤拷(1)锟斤拷锟饺測(c锟斤拷)锟斤拷(hu锟斤拷)直锟絕锟紻锟斤拷要锟斤拷

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锟斤拷锟�锟斤拷锟斤拷锟酵队帮拷D锟斤拷取锟斤拷(xi锟斤拷n)锟斤拷锟絃(zh锟斤拷ng)锟饺的凤拷锟斤拷锟角ｏ拷锟斤拷锟斤拷锟絊锟较伙拷平锟斤拷锟斤拷锟斤拷锟絊锟侥撅拷(xi锟斤拷n)锟轿讹拷取锟斤拷(sh锟斤拷)锟絃(zh锟斤拷ng)锟斤拷

锟斤拷锟斤拷锟紷锟斤拷锟絚斜锟斤拷锟統(c锟斤拷)锟斤拷(hu锟斤拷)直锟絕锟紻锟侥凤拷锟斤拷锟斤拷同锟斤拷要注锟斤拷锟斤拷锟斤拷锟侥區(q锟斤拷)锟絜锟斤拷

锟斤拷锟斤拷(2)锟斤拷锟饺測(c锟斤拷)锟紸锟斤拷锟斤拷锟紸锟紽锟斤拷锟紸锟絖(t锟斤拷i)锟斤拷直锟絕锟紻锟侥區(q锟斤拷)锟絜锟斤拷要锟斤拷水平锟斤拷锟矫碉拷平锟斤拷D锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷锟饺測(c锟斤拷)锟斤拷(hu锟斤拷)水平锟斤拷锟矫碉拷平锟斤拷A锟轿時(sh锟斤拷)锟斤拷锟斤拷X锟絊锟斤拷(hu锟斤拷)锟斤拷水平位锟斤拷锟斤拷Y锟絊锟斤拷(hu锟斤拷)锟斤拷锟絚X锟絊锟斤拷120°锟斤拷锟斤拷投影锟紻锟较ｏ拷X锟絊锟斤拷Y锟絊锟斤拷锟斤拷锟斤拷锟絚X锟絊锟斤拷Y锟絊平锟叫的撅拷(xi锟斤拷n)锟轿讹拷取锟斤拷(sh锟斤拷)锟絃(zh锟斤拷ng)锟斤拷锟斤拷Z锟絊锟较伙拷锟絚Z锟絊平锟叫的撅拷(xi锟斤拷n)锟轿的�锟�(hu锟斤拷)锟斤拷锟絚斜锟斤拷锟統(c锟斤拷)锟斤拷同锟斤拷也锟斤拷取锟斤拷(sh锟斤拷)锟絃(zh锟斤拷ng)锟斤拷

锟斤拷锟斤拷5.锟絇(gu锟斤拷n)锟节幾猴拷锟絯锟斤拷锟斤拷锟�(n锟斤拷i)锟斤拷锟絚(di锟斤拷n)锟絞锟斤拷锟斤拷叹锟斤拷x锟斤拷(w锟斤拷n)锟絵

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锟斤拷锟斤拷锟絇(gu锟斤拷n)锟斤拷锟絔锟斤拷

       锟竭讹拷锟斤拷(sh锟斤拷)锟絎(xu锟斤拷)锟斤拷(f锟斤拷)锟斤拷(x锟斤拷)锟斤拷锟斤拷锟絉锟斤拷

锟斤拷锟铰高匡拷锟結訊锟斤拷锟竭匡拷锟斤拷锟斤拷锟斤拷锟斤拷前锟斤拷(zh锟斤拷n)锟斤拷锟斤拷志愿锟斤拷锟�(b锟斤拷o)锟斤拷锟饺★拷锟�?j锟斤拷n)?sh锟斤拷)锟斤拷(xi锟斤拷n)锟斤拷

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锟組锟斤拷"锟竭匡拷锟絎(w锟斤拷ng)"微锟脚癸拷锟斤拷號(h锟斤拷o)