Question

Assertion (A): The length of the arc of a sector of a circle with radius $$14\ \text{cm}$$ and of central angle $$60^{\circ}$$ is $$\frac{88}{3}\ \text{cm}$$.

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

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. Using the stated arc-length formula:

\[\text{Arc length}=\frac{2\pi r\theta}{360}\]

\[=\frac{2\times\frac{22}{7}\times14\times60}{360}\ \text{cm}\]

\[=\frac{44}{3}\ \text{cm}\]

This is not $$\frac{88}{3}\ \text{cm}$$.

Step 2 – Reason: R is true. The formula given in the reason correctly gives the arc length for a circle of radius $$r$$ and central angle $$\theta$$.