Home
Class 12
MATHS
A wire of length 2 units is cut into two...

A wire of length 2 units is cut into two parts which are bent respectively to form a square of `s i d e=x` units and a circle of `r a d i u s=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) `(pi+4)x=pir` (3) `x=2r` (4) `2x=r`

A

`(4-pi)x=pir`

B

x=2r

C

2x=r

D

`2x=(pi+4)r`

Text Solution

Verified by Experts

The correct Answer is:
2
we have `4x+2pir=2`
Now sum of areas of square and circle is `x^(2)+pir^(2)`
`rarr f(R )=(1-pir)/(2)+pir^(2)`
`rarr (df(r ))/(dr)=2(pir-1)/(2)(pi)/(2)+2pir`
`(df(r ))/(dr)=0`
`rarr r=(1)/(pi+4)`
from `1, 2x=(4)/(pi+4)`
`rarr x=2r`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|17 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Numerical)|20 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

A wire of length 2 units is cut into two parts which are bent respectively to from a square ofside c units and a circle of radius r units if the sum of the sum of the areas of the square and the circle so fromed is minimum then

A wire of length a is cut into two parts which are bent,respectively,in the form of a square and a circle.The least value of the sum of the areas so formed is (a^(2))/(pi+4) (b) (a)/(pi+4)(a)/(4(pi+4)) (d) (a^(2))/(4(pi+4))

A wire of length l is cut into two parts. One part is bent into a circle of radius r and other part into a square of side x. The sum of areas of circle and square is least, if

The equation of a circle of area 22pi square units for which each of the two lines 2x + y = 2 and x-y =- 5 is diameter, is :

If the lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.

If the radius ( r ) of a circle is increased by 'x' units , what is the number of units by which the circumference of the circle is increased? A. pi B. 2pi C. 2pi r D. 2pi x

By using intergration prove that the area of a circle of radius r units is pir^2 square units.

If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49 pi square units,the equation of the circle is: