A wire of length 2 units is cut into two parts which are bent respectively to form a…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

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)

2x = (\pi + 4)r

(2)

(4 - \pi)x = \pi r

(3)

x = 2r

(4)

2x = r