Question : If the circumference of a circle is equal to the perimeter of a square, and the radius of the given circle is positive, then which of the following options is correct?
Option 1: Area of the circle > Area of the square
Option 2: Area of the circle
Option 3: Area of the circle < Area of the square
Option 4: Area of the circle = Area of the square
Correct Answer: Area of the circle > Area of the square
Solution :
Let the radius of the circle be '
Since the perimeter of a square = circumference of a circle
⇒ 4a = 2
⇒ a =
⇒ Area of Square =
⇒
So, the area of the circle > the area of the square.
Hence, the correct answer is Area of the circle > Area of the square.
