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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: (1) (4-π)x = πr (2) x = 2r (1) 2x = r (2) 2x = (π + 4)r?
Verified Answer
A wire of length 2 units is cut into two parts which are bent respecti...
Given that 4x + (2 x pi x r) = 2 
i.e. 2x + pi x r = 1 
r = (1-2x)/pi     --(i) 
 
Area A = x^2 + pi x r^2 
= x^2 + 1/pi(2x - 1)^2 

for min value of area A;
dA/dx=0 gives x = 2/(pi + 4) --(ii)

From (i) and (ii)
r = 1/(pi + 4) 
So,
x = 2r 

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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: (1) (4-π)x = πr (2) x = 2r (1) 2x = r (2) 2x = (π + 4)r?
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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: (1) (4-π)x = πr (2) x = 2r (1) 2x = r (2) 2x = (π + 4)r? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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: (1) (4-π)x = πr (2) x = 2r (1) 2x = r (2) 2x = (π + 4)r? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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: (1) (4-π)x = πr (2) x = 2r (1) 2x = r (2) 2x = (π + 4)r?.
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