Question

Assertion (A) : In a circle of radius 21 cm, an arc of length 22 cm subtends an angle of 60\(^\circ\) at the centre.
Reason (R) : The length of arc of a sector of a circle of radius r and central angle \(\theta\) is \(\frac{2\pi r\theta}{360}\).

• A. Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
• B. Both, Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

For Assertion-Reason questions, always write down the verification calculation explicitly.
This establishes the logical link between both statements clearly!

Answer 1

The Correct Option is A

Step 1: Rewrite the arc-length formula in radian form.
The reason's formula is equivalent to $l = r\theta$ when $\theta$ is measured in radians, and $60^\circ = \frac{\pi}{3}$ radians.
Step 2: Check the Assertion using this radian form.
\[ l = 21 \times \frac{\pi}{3} = 7\pi \approx 7 \times \frac{22}{7} = 22 \text{ cm} \]
This matches the 22 cm stated in the Assertion, so the Assertion is true.
Step 3: Confirm the Reason correctly explains it.
Since converting the Reason's formula gave exactly the number in the Assertion, the Reason is the correct explanation of the Assertion.
\[ \boxed{\text{Both A and R are true, and R correctly explains A}} \]