Question

Assertion (A): The radius of a circle in which a central angle of 60 degrees intercepts an arc length of 37.4 cm (using \( \pi = \frac{22}{7} \))
Reason (R): The formula to calculate the length of an arc is \( l = Q \times r \), where \( l \) is the arc length, \( Q \) is the central angle in radians, and \( r \) is the radius of the circle.

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

Hint:

Remember the formula for the arc length: \( l = Q \times r \), where \( Q \) is in radians and \( r \) is the radius.

Answer 1

The Correct Option is A

Step 1: Assertion (A) analysis.
The formula for the length of an arc is given by \( l = Q \times r \), where \( Q \) is the central angle in radians and \( r \) is the radius of the circle. Since the central angle is 60 degrees, we need to convert it to radians using \( Q = \frac{60 \times \pi}{180} = \frac{\pi}{3} \). The formula holds true for finding the arc length.
Step 2: Reason (R) analysis.
Reason (R) is also correct, as it provides the correct formula to calculate the length of an arc, and the formula matches the calculation for the arc length in Assertion (A).
Step 3: Conclusion.
Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct explanation of Assertion (A). Final Answer:} (A) Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct explanation of Assertion (A).