A rectangular block is heated from `0^(@)C` to `100^(@)C`. The percentage increase in its length is `0.2%` . The percentage increase in its volume is

Options

A. `0.6%`
B. `0.10%`
C. `0.2%`
D. `0.4%`

Explanation

To find the percentage increase in the volume of a rectangular block when it is heated, we can use the relationship between the change in length and the change in volume.

### Step-by-Step Solution:

1. **Understand the relationship between length and volume**:
- The volume \( V \) of a rectangular block can be expressed as \( V = L^3 \) where \( L \) is the length of the block.

2. **Define the percentage change in volume**:
- The percentage change in volume can be expressed as:
\[ \frac{\Delta V}{V} \times 100 \]
- Where \( \Delta V \) is the change in volume.

3. **Relate the change in volume to the change in length**:
- When the block is heated, the change in volume can be related to the change in length by the formula:
\[ \frac{\Delta V}{V} = 3 \frac{\Delta L}{L} \]
- This means that the percentage change in volume is three times the percentage change in length.

4. **Substitute the given values**:
- We are given that the percentage increase in length \( \frac{\Delta L}{L} \times 100 = 0.2\% \).
- Therefore, we can substitute this value into the equation:
\[ \frac{\Delta V}{V} \times 100 = 3 \times 0.2\% \]

5. **Calculate the percentage increase in volume**:
- Now, calculate the percentage increase in volume:
\[ \frac{\Delta V}{V} \times 100 = 0.6\% \]

6. **Conclusion**:
- The percentage increase in the volume of the rectangular block when heated from \( 0^\circ C \) to \( 100^\circ C \) is \( 0.6\% \).

### Final Answer:
The percentage increase in its volume is \( 0.6\% \).

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