Question 5 - NCERT Exemplar - MCQ - Chapter 12 Class 10 Areas related to Circles (Term 1)

Transcript

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)