Question 5
If the circumference of a circle and the perimeter of a square are equal, then
(A) Area of the circle = Area of the square
(B) Area of the circle > Area of the square
(C) Area of the circle < Area of the square
(D) Nothing definite can be said about the relation between the areas of the circle and square.
Let Radius of circle = r
Side of square = a
Now, given that
Circumference of Circle = Perimeter of Square
2๐r = 4a
๐r = 2a
2a = ๐r
a = ๐ /๐ ๐
Now, we need to find relation between Area of square and circle
Area of circle = ๐๐^2
Circle
Area of circle = ๐ ๐^๐
Square
Area of square = a2
= (๐/2 ๐)^2
= ๐ ^๐/๐ ๐^๐
Since ๐ ๐^๐ > ๐^2/4 ๐^2
Therefore,
Area of the circle > Area of the square
So, the correct answer is (B)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.