1. A wire of length 2 units is cut into two parts

Question

1. 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:

Samyak Jain · Accepted Answer

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. Perimeter of square = 4x & perimeter of circle (i.e. its circumference) = 2r So sum of perimeters of given figures is equal to 2, i.e., 4x + 2r = 2 or x = (1 &ndash; r)/2 Sum of areas of the square & the circle = x2 + r2 , Put x = (1 &ndash; r)/2 = [(1 &ndash; r)/2]2 + r2 = (1 &ndash; 2r + 2 r2)/4 + r2 = (1/4)[1 &ndash; 2r + 2 r2 +4r2] Differentiate the above expression wrt x and equate it to zero. (1/4)[0 &ndash; 2 + 2 2r + 4.2r] = 0 => &ndash; 2 + 2 2r + 4.2r = 0 2(2 + 4) r = 2 => r = / (2 + 4) = 1/( + 4) Differentiate (1/4)[0 &ndash; 2 + 2 2r + 4.2r] to check the value of r we got is minimum or maximum. We get (1/4)[0 &ndash; 0 + 22 + 8] > 0. Thus, minima is formed. x = (1 &ndash; r)/2 , x = (1 &ndash; / + 4)/2 = ( + 4 &ndash; ) / 2( + 4) x = 4/2( + 4) = 2 / + 4 x = 2 / ( + 4) & r = 1/( + 4) . If satisfied with my answer, pls approve it.

Algebra> 1. A wire of length 2 units is cut into t...

1. 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. 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:

Narendra , 7 Years ago

Samyak Jain

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.

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Algebra> 1. A wire of length 2 units is cut into t...

1. 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. 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:

Narendra , 7 Years ago

Samyak Jain

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.

LIVE ONLINE CLASSES

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