Question

Assertion (A): If a sector of a circle with central angle $$60^{\circ}$$ has an area $$924\ \text{cm}^{2}$$ then the radius of the circle is $$42\ \text{cm}$$.

Reason (R): The sum of the areas of a major sector of a circle and its corresponding minor sector is equal to the area of the circle.

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 but Reason (R) is not a correct explanation of Assertion (А).

Explanation:

Step 1 – Assertion: A is true. Using the sector-area formula, $$\pi r^{2}\times\frac{60}{360} = 924\ \text{cm}^{2}$$. With $$\pi = \frac{22}{7}$$, this gives $$r^{2} = 1764\ \text{cm}^{2}$$, so $$r = 42\ \text{cm}$$.

Step 2 – Reason: R is true. A major sector and its corresponding minor sector together make the whole circle.

Step 3 – Link: The reason describes the relationship between complementary sectors; it does not establish the radius from the given minor-sector area and angle.