Question

Assertion (A): If the circumferences of two circles are in the ratio $$5 : 6$$ then the ratio of their radii is $$5 : 6$$.

Reason (R): The circumference of a circle is directly proportional to the square of the radius of the circle.

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 true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. Since the circumference is $$2\pi r$$, the ratio of circumferences equals the ratio of the radii. Hence the radii are in the ratio $$5 : 6$$.

Step 2 – Reason: R is false. Circumference is directly proportional to the radius, not to the square of the radius.