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
2𝜋r = 4a
𝜋r = 2a
2a = 𝜋r
a = 𝝅/𝟐 𝒓
Now, we need to find relation between Area of square and circle
Area of circle = 𝜋𝑟^2
Circle
Area of circle = 𝝅𝒓^𝟐
Square
Area of square = a2
= (𝜋/2 𝑟)^2
= 𝝅^𝟐/𝟒 𝒓^𝟐
Since 𝝅𝒓^𝟐 > 𝜋^2/4 𝑟^2
Therefore,
Area of the circle > Area of the square
So, the correct answer is (B)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.