Question

Assertion (A): The surface area of the largest sphere that can be inscribed in a hollow cube of side $$a\ \mathrm{cm}$$ is $$\pi a^{2}\ \mathrm{cm}^{2}$$.

Reason (R): The surface area of a sphere of radius $$r$$ is $$\frac{4}{3}\pi r^{3}$$.

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 true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. The largest inscribed sphere has diameter $$a$$ and radius $$\frac{a}{2}$$. Its surface area is $$4\pi\left(\frac{a}{2}\right)^{2} = \pi a^{2}$$.

Step 2 – Reason: R is false. The expression $$\frac{4}{3}\pi r^{3}$$ is the volume of a sphere, not its surface area. The surface area is $$4\pi r^{2}$$.

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