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 an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.
Many students prefer Teachoo Black for a smooth, ad-free learning experience.
It looks like you're using AdBlock
Don't be a miser! Join Teachoo Black at ₹19 only to view the ad-free version of Teachoo.
Please login to view more pages. It's free :)
Teachoo gives you a better experience when you're logged in. Please login :)