Question

Assertion (A): The area of the sector of a circle of radius $$14\ \text{cm}$$ and central angle $$90^{\circ}$$ is $$154\ \text{cm}^{2}$$.

Reason (R): The area of the sector of a circle of radius $$r$$ cm and central angle $$\theta$$ is $$\left(\pi r^{2}\frac{\theta}{360}\right)\ \text{cm}^{2}$$.

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

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

Explanation:

Step 1 – Assertion: A is true. Substituting $$r=14\ \text{cm}$$, $$\theta=90^{\circ}$$ and $$\pi=\frac{22}{7}$$ gives $$\frac{22}{7}\times14^{2}\times\frac{90}{360}=154\ \text{cm}^{2}$$.

Step 2 – Reason: R is true. The area of a sector is the fraction $$\frac{\theta}{360}$$ of the circle’s area, giving the stated formula.

Step 3 – Link: The reason’s formula directly gives the asserted area when the given values are substituted.