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`

`2x=(pi+4)r`

`(4-pi)x=pi r`

`x=2r`

`2x =r`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATION OF DEFINITEINTEGRAL
NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS:(MCQ)|27 Videos
BINOMIAL DISTRIBUTION
NIKITA PUBLICATION|Exercise MCQS|77 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:

NIKITA PUBLICATION-APPLICATIONS OF DERIVATIVES-MULTIPLE CHOICE QUESTIONS

A metal wire of 36 cm long is bent to form a rectangle. Find its dimen...
Text Solution
|
A wire of length l is cut into two parts. One part is bent into a circ...
Text Solution
|
A wire of length 2 units is cut into two parts which are bent respe...
Text Solution
|
A rectangle is inscribed in a semicircle of radius 1 unit. If its two ...
Text Solution
|
A window is in the form of a rectangle surmounted by a semi-circle....
Text Solution
|
A rectangular sheet of paper has the area 24 sq. meters. The margin at...
Text Solution
|
If a rectangle of maximum area is inscibed in the ellipse (x^(2))/(a^(...
Text Solution
|
Twenty metres of wire is available for fencing off a flower-bed in ...
Text Solution
|
If P is the perimeter and r is the radius of a sector, then the area o...
Text Solution
|
From a square cardboard of side 18 cms an open tank is made by cutting...
Text Solution
|
From a metal sheet of area 192 sq. cm, a box with square base and open...
Text Solution
|
Determine the points on the curve x^2=4y which are nearest to th...
Text Solution
|
The shortest distance between line y-x=1 and curve x=y^2 is
Text Solution
|
A right circular cone have slant height 3 cm. Then its volume is maxim...
Text Solution
|
The height of the cone of maximum volume inscribed in a sphere of radi...
Text Solution
|
An open cylindrical tank whose base is a circle is to be constructed o...
Text Solution
|
Find the maximum volume of right circular cylinder, if the sum of its...
Text Solution
|
If h is the height and r is the base radius of an open right circular ...
Text Solution
|
The point on the curve y= sqrt(x-1) where the tangent is perpen...
Text Solution
|
The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve i...
Text Solution
|