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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:?
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A wire of length 2 units is cut into two parts which are bent respecti...
Perimeter of square =4x
perimeter of circle = 2πr
Therefore 4x+2πr=2
r=(2-4x)/2π.(I)
Now area formed by both square and circle is minimum
x^2+πr^2=minimum.ii
sub I in ii
x^2+π(2-4x)^2/4π^2=min
x^2+(2-4x)^2/4π=min
On to calculus!
Let f(x)=x^2+(2-4x)^2/4π
f'(x) =2x+8(4x-2)/4π
=2x+2(4x-2)/π
f'(x)=0
2x+2(4x-2)/π=0
2πx-4+8x=0
(2π+8)x=4
x=4/2π+8
=2/(π+4)
=0.28
Thus when the length of the square is 0.28 units then the sum of the areas formed by the circle and square is minimum.
perimeter of circle = 2πr
Therefore 4x+2πr=2
r=(2-4x)/2π.(I)
Now area formed by both square and circle is minimum
x^2+πr^2=minimum.ii
sub I in ii
x^2+π(2-4x)^2/4π^2=min
x^2+(2-4x)^2/4π=min
On to calculus!
Let f(x)=x^2+(2-4x)^2/4π
f'(x) =2x+8(4x-2)/4π
=2x+2(4x-2)/π
f'(x)=0
2x+2(4x-2)/π=0
2πx-4+8x=0
(2π+8)x=4
x=4/2π+8
=2/(π+4)
=0.28
Thus when the length of the square is 0.28 units then the sum of the areas formed by the circle and square is minimum.
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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:?
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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:? 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:? 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:?.
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:? 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:? 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:?.
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