Question

如圖在圓形大廳的頂部四周安裝了若干個(gè)監(jiān)控器，每個(gè)監(jiān)控器監(jiān)控的角度是55°，則至少要安裝________個(gè)監(jiān)控器才能監(jiān)控到整個(gè)大廳．

Answer 1

4
分析：由圖可知掃射到的圓弧對(duì)應(yīng)的圓心角為110°，而圓周角為360°，所以至少得4個(gè)監(jiān)控器才可以．
解答：解；∵圖中監(jiān)控器掃射范圍對(duì)應(yīng)的圓周角為55°
∴它對(duì)應(yīng)的圓心角為110°
要想監(jiān)控到每一個(gè)角度，監(jiān)控范圍所對(duì)應(yīng)的圓心角之和得大于或等于360°
所以至少得4個(gè)監(jiān)控器．
點(diǎn)評(píng)：本題考查了圓的認(rèn)識(shí)，做題中注意圓周角、圓心角知識(shí)的利用．