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3m. What is10 A piece of wire is of length sm. It is cut into two pieces. The length of one piece is 4the length of the other piece?71116 |
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Answer» Answer: Length of wire =50 m (Given) Let length of one piece for shape of square =x m ∴ Length of other piece for shape of circle =(50−x)m Now PERIMETER of square =4a=x ⇒a= 4 x
and circumference of circle =2πr=50−x ⇒r= 2π 50−x
2 +πr 2
= 16 x 2
+π⋅( 2π 50−x
) 2
= 16 x 2
+π⋅ 4π 2
(50−x) 2
A= 16 x 2
+ 4π (50−x) 2
Differentiating w.r. to x, we get dx dA
= 16 2x
+ 4π 2(50−x)(−1)
dx dA
= 8 x
+ 2π (x−50)
= 8π πx+4x−200
= 8π x(4+π)−200
For extremum, dx dA
=0 ∴x(4+π)−200=0 x= 4+π 200
dx 2
d 2 A
>0 A is minimum at x= 4+π 200
∴ Length of square of square wire, x= 4+π 200
m and length of circle wire =50−x =50− 4+π 200
= 4+π 50π
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