JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q73

← JEE Main 2016 · 3 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 73 of 90

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 :

2x=(\pi+4)r

(4-\pi)x=\pi r

x=2r

2x=r

Answer and worked solution

Official answer: C

$4x+2\pi r=2$ and $A=x^2+\pi r^2$ . With $\frac{dx}{dr}=-\frac\pi2$ : $\frac{dA}{dr}=-\pi x+2\pi r=0$ , so $x=2r$ .

Topics:Maxima and minima

← Previous question Next question →

JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 73