Question

Assertion (A): If the radius of a circle is tripled then the resulting percentage increase in the area of the circle is $$900\%$$.

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

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. Tripling the radius multiplies the area by $$3^{2} = 9$$. Therefore, the increase is $$9A - A = 8A$$, which is an $$800\%$$ increase, not $$900\%$$.

Step 2 – Reason: R is true. The area formula is $$A = \pi r^{2}$$, so area is directly proportional to the square of the radius.