If the circumference of a circle and the perimeter of a square are equal, then
Area of the circle = Area of the square
Area of the circle > Area of the square
Area of the circle < Area of the square
Nothing definite can be said about the relation between the areas
Step 1: Let the radius of the circle be r (in metres).
Then, circumference of the circle = \(2 \pi r\) metres.
Step 2: Let the side of the square be a (in metres).
Then, perimeter of the square = \(4a\) metres.
Step 3: It is given that circumference of the circle = perimeter of the square.
So, \(2 \pi r = 4a\).
Step 4: Solve for a:
\(a = \dfrac{2 \pi r}{4} = \dfrac{\pi r}{2}\).
Step 5: Find the area of the circle:
Area of circle = \(\pi r^2\) (square metres).
Step 6: Find the area of the square:
Area of square = \(a^2 = \left(\dfrac{\pi r}{2}\right)^2 = \dfrac{\pi^2}{4}r^2\) (square metres).
Step 7: Compare the two areas:
Step 8: Numerical values:
\(\pi \approx 3.14\).
\(\dfrac{\pi^2}{4} \approx \dfrac{9.87}{4} = 2.47\).
So, \(3.14 r^2 > 2.47 r^2\).
Final Step: The area of the circle is greater than the area of the square.
Correct Option: (B)