Given that 4x+2πr=2
i.e., 2x+πr=1
∴ r=π1−2x .......(i)
Area A=x2+πr2
=x2+π1(2x−1)2
For min vale of area A
dxdA=0 gives x=π+42 .......(ii)
From (i) and (ii)
r=π+41 .......(iii)
∴ x=2r
A wire of length 2 units is cut into two parts which are bent respectively to form a square of side =x units and a circle of radius =r units. If the sum of the areas of the square and the circle so formed is minimum, then
Held on 3 Apr 2016 · Verified 6 Jul 2026.
x=2r
2x=r
2x=(π+4)r
(4−π)x=πr
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