Question

Assertion (A): The area of the sector of a circle of radius $$21\ \text{cm}$$ cut-off by an arc of length $$22\ \text{cm}$$ is $$231\ \text{cm}^{2}$$.

Reason (R): The angle subtended by the arc at the centre of the circle is $$30^{\circ}$$.

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. The sector’s area is half the product of its radius and arc length: $$\frac{1}{2}\times21\times22 = 231\ \text{cm}^{2}$$.

Step 2 – Reason: R is false. The arc length formula gives $$\frac{2\pi(21)\theta}{360} = 22\ \text{cm}$$, which yields $$\theta = 60^{\circ}$$, not $$30^{\circ}$$.