Question

用铁丝围成一个上面是半圆,下面市矩形的图形,其面积为a,为使所用材料最省,底 视频

Answer 1

设半圆半径为r,则矩形的一边是2r,设另一边为b.

пr^2+2rb=a

b=(a-пr^2)/2r

铁丝长度=半圆周长+2r+2b

=пr+2r+(a-пr^2)/r

=пr+2r+a/r-пr

=2r+a/r

2r=a/r时,长度最小

2r^2=a

r=√2a/2