The lengths of sides of a cuboid are a, 2a and 3a. If the relative percentage error in the measurement of a is `1%`, then what is the relative percentage error in the measurement of the volume of the cuboid.

Answer

To solve the problem, we need to determine the relative percentage error in the volume of a cuboid given the lengths of its sides and the relative percentage error in one of its dimensions.

### Step-by-Step Solution:

1. **Identify the dimensions of the cuboid**:
The lengths of the sides of the cuboid are given as \( a \), \( 2a \), and \( 3a \).

2. **Calculate the volume of the cuboid**:
The volume \( V \) of a cuboid is calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the dimensions:
\[ V = a \times 2a \times 3a = 6a^3 \]

3. **Determine the relative percentage error in the measurement of \( a \)**:
We are given that the relative percentage error in the measurement of \( a \) is \( 1\% \). This can be expressed as:
\[ \frac{\Delta a}{a} \times 100\% = 1\% \]
where \( \Delta a \) is the absolute error in \( a \).

4. **Relate the error in volume to the error in \( a \)**:
The volume \( V \) depends on \( a \). Since \( V = 6a^3 \), we can find the relative error in \( V \) using the formula for propagation of errors. The relative error in volume can be expressed as:
\[ \frac{\Delta V}{V} \times 100\% = 3 \times \frac{\Delta a}{a} \times 100\% \]
This is because the volume is proportional to \( a^3 \), and thus the error in volume is three times the error in \( a \).

5. **Substitute the known values**:
Since we know that \( \frac{\Delta a}{a} \times 100\% = 1\% \), we can substitute this into the equation:
\[ \frac{\Delta V}{V} \times 100\% = 3 \times 1\% = 3\% \]

6. **Conclusion**:
Therefore, the relative percentage error in the measurement of the volume of the cuboid is:
\[ \boxed{3\%} \]