If the circumference of a circle and the perimeter of a square are equ

1.	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 & square.
Answer» (B) Area of the circle > Area of the square Explanation: According to the question, Circumference of a circle = Perimeter of square Let r be the radius of the circle and a be the side of square. ∴ From the given condition, we have 2π r = 4a (22/7)r = 2a ⇒ 11r = 7a ⇒ a = (11/7)a ⇒ r = (7/11)a …………..(i) Now, area of circle = A₁ = πr² and area of square = A₂ = a² From equation (i ), we have A₁ = π × (7/11)² = (22/7) × (49/121)a² = (14/11)a² and A₂ = a² ∴ A₁ = (14/11) A₂ ⇒ A₁ > A₂ Hence, Area of the circle > Area of the square. ∴ Option B is correct.

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 & square.

Answer»

(B) Area of the circle > Area of the square

Explanation:

According to the question,

Circumference of a circle = Perimeter of square

Let r be the radius of the circle and a be the side of square.

∴ From the given condition, we have 2π r = 4a

(22/7)r = 2a

⇒ 11r = 7a

⇒ a = (11/7)a

⇒ r = (7/11)a …………..(i)

Now, area of circle = A₁ = πr² and area of square = A₂ = a²

From equation (i ), we have

A₁ = π × (7/11)²

= (22/7) × (49/121)a²

= (14/11)a² and A₂ = a²

∴ A₁ = (14/11) A₂

⇒ A₁ > A₂

Hence, Area of the circle > Area of the square.

∴ Option B is correct.