15.一个正四棱柱的各个顶点在一个直径为2cm的球面上。如果正四棱柱

15.一个正四棱柱的各个顶点在一个直径为2cm的球面上。如果正四棱柱的底面边长为1cm,那么该棱柱的表面积为      cm2.

答案

解析:方法一:由已知正四棱柱体对角线即为球直径,

设正四棱柱高为h,则2+h2=4,

h=.∴.

方法二:由已知,R=1,r=,

d=.

=2d=.

=2×12+4×(1×)=2+.


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