Question

Assertion (A): If the radius of a semicircular protractor is $$7\ \text{cm}$$ then its perimeter is $$36\ \text{cm}$$.

Reason (R): The perimeter of a semicircular protractor of radius $$r$$ cm is $$r(\pi + 2)$$ 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

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 $$r = 7\ \text{cm}$$ and $$\pi = \frac{22}{7}$$ into the perimeter formula gives $$7\left(\frac{22}{7} + 2\right) = 36\ \text{cm}$$.

Step 2 – Reason: R is true. The perimeter consists of the semicircular arc and its diameter, giving $$\frac{1}{2}(2\pi r) + 2r = r(\pi + 2)$$.

Step 3 – Link: The reason gives the formula used to find the protractor’s perimeter, so it correctly explains the assertion.