The sum of the perimeter of a circle and...

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

Topper's Solved these Questions

APPLICATIONS OF DERIVATIVES
MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos
APPLICATIONS OF DERIVATIVES
MODERN PUBLICATION|Exercise COMPLETITION FILE (Questions from JEE Main)|18 Videos
APPLICATIONS OF DERIVATIVES
MODERN PUBLICATION|Exercise Exercise|15 Videos
APPLICATIONS OF THE INTEGRALS
MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

The sum of the perimeters of a circle and a square is k, where k is some constant.Prove that the sum of their areas is least when the side of the square is double the radius of the circle.

The sum of perimeter of a square and circumference of a circle is given. Prove that the sum of their areas will be minimum when the side of square is equal to the diameter of the circle.

If the side of a square is doubled, then the area of the square

Given the sum of the perimeters of a square and a circle,show that the sum of their areas is least when one side of the square is equal to diameter of the circle.

Area of a square is doubled if the side of the square is doubled.

A wire of length l is cut into two parts. One part is bent into a circle and the other into a square. Prove that the sum of the areas of the circle and the square is the least, if the radius of the circle is half of the side of the square.

The area of a square is equal to the area of a circle. What is the ratio between the side of the square and the radius of the circle?

A circle and a square have same area. The ratio of the side of the square to the radius of the circle will be :

The areas of a circle and a square are same. The ratio of the side of the square to the radius of the circle is

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-Revision Exercise

The equation of the tangent at (2,3) on the curve y^2=a x^3+b is y=4x-...
Text Solution
|
A circular disc of radius 3 cm is being heated. Due to expansion, i...
Text Solution
|
The radius of a sphere shrinks from 10 to 9.8 cm. Find approximatel...
Text Solution
|
If the error committed in measuring the radius of a circle is 0.01%, f...
Text Solution
|
If a triangle ABC, inscribed in a fixed circle, be slightly varied in ...
Text Solution
|
The area S of a triangle is calculated by measuring the sides b and c,...
Text Solution
|
The pressure p and the volume v of a gas are connected by the relat...
Text Solution
|
Show that the function given by f(x)=(logx)/xhas maximum at x = e.
Text Solution
|
The sum of the perimeter of a circle and square is k, where k is so...
Text Solution
|
Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...
Text Solution
|
Show that s in^p\ theta\ cos^q\ theta attains a maximum, when theta...
Text Solution
|
The fraction exceeds its p^(th) power by the greatest number possible...
Text Solution
|
If the sum of the lengths of the hypotenues and a side of a right a...
Text Solution
|
Divide 4 into two positive numbers such that the sum of the square of ...
Text Solution
|
A cylindrical can to be made to hold 1 litres of oil. Find the dimensi...
Text Solution
|
Find the shortest distance of the point (0, c) from the curve y=x^(2),...
Text Solution
|
A beam of length l is supported at one end. If W is the uniform loa...
Text Solution
|
Find the maximum area of an isosceles triangle inscribed in the ellip...
Text Solution
|
Find the area of the greatest rectangle that can be inscribed in an...
Text Solution
|
A window of perimeter P (including the base of the arch) is in the ...
Text Solution
|