Question

Assertion (A): The volume of the largest sphere carved out of a solid cube of side 21 cm is $$4851\ \mathrm{cm}^{3}$$.

Reason (R): The radius of the largest sphere carved out of a solid cube is half the side of the cube.

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

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. The largest sphere has radius $$\frac{21}{2}\ \mathrm{cm}$$. Its volume is: $$V = \frac{4}{3}\times\frac{22}{7}\times\left(\frac{21}{2}\right)^{3}$$ $$V = 4851\ \mathrm{cm}^{3}$$

Step 2 – Reason: R is true. The diameter of the largest sphere equals the cube’s side, so its radius is half the side.

Step 3 – Link: The reason gives the sphere’s radius, which is used in the sphere-volume formula to obtain the value in A; therefore, R correctly explains A.