Question

Assertion (A): The area of a semicircle of diameter $$d$$ is $$\frac{1}{8}\pi d^{2}$$.

Reason (R): The central angle of a semicircle is $$90^{\circ}$$.

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 true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. The area of a semicircle is half the area of a circle. Using $$r=\frac{d}{2}$$ gives $$\frac{1}{2}\pi\left(\frac{d}{2}\right)^{2}=\frac{1}{8}\pi d^{2}$$.

Step 2 – Reason: R is false. The central angle of a semicircle is $$180^{\circ}$$, not $$90^{\circ}$$.