Question

Assertion (A): 168 spherical shots of diameter 3 cm each can be made by melting a cuboidal solid of dimensions $$18\ \mathrm{cm} \times 22\ \mathrm{cm} \times 6\ \mathrm{cm}$$.

Reason (R): Total volume of the spherical shots = volume of the cuboidal solid.

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. Each shot has radius $$\frac{3}{2}\ \mathrm{cm}$$. The number of shots is the cuboid’s volume divided by one shot’s volume: $$\frac{18 \times 22 \times 6}{\frac{4}{3} \times \frac{22}{7} \times \left(\frac{3}{2}\right)^{3}} = 168$$

Step 2 – Reason: R is true. When the solid is melted, its volume is conserved; thus, the total volume of the spherical shots equals the cuboid’s volume.

Step 3 – Link: This volume equality is the principle used to calculate the number of shots, so R correctly explains A.