Question

Assertion (A): The diameter of a sphere, whose surface area is $$616\ \mathrm{cm}^{2}$$, is 7 cm.

Reason (R): The surface area of a sphere of radius $$r$$ is $$4\pi r^{2}$$.

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 (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. Using the given surface area and the sphere formula: $$4\pi r^{2} = 616$$ $$r^{2} = 49\ \mathrm{cm}^{2}, r = 7\ \mathrm{cm}$$ $$\text{Diameter} = 2r = 14\ \mathrm{cm}$$

Step 2 – Reason: R is true. The surface area of a sphere of radius $$r$$ is $$4\pi r^{2}$$.

Therefore, the correct option is: Assertion (A) is false and Reason (R) is true.