Question

Assertion (A): If a circle and a square have the same perimeter then the area of the square is greater than the area of the circle.

Reason (R): If the radius of the circle is $$r$$ and the side of the square is $$s$$, then $$r = \frac{2s}{\pi}$$.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (А).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. For equal perimeters, the circle’s radius is $$r = \frac{2s}{\pi}$$. Its area is $$\pi r^{2} = \frac{4s^{2}}{\pi}$$, which is greater than the square’s area $$s^{2}$$ because $$\frac{4}{\pi} > 1$$.

Step 2 – Reason: R is true. Equating the perimeters, $$2\pi r = 4s$$, gives $$r = \frac{2s}{\pi}$$.