A cuboid has volume `V=lxx2lxx3l`, where l is the length of one side. If the relative percentage error in the measurment of l is 1%, then the relative percentage error in measurement of V is

Options

A. 0.18
B. 0.06
C. 0.03
D. 0.01

Explanation

To solve the problem, we need to find the relative percentage error in the volume \( V \) of a cuboid when the relative percentage error in the measurement of the length \( l \) is given as 1%.

### Step-by-Step Solution:

1. **Understand the Volume Formula**:
The volume \( V \) of the cuboid is given by the formula:
\[ V = l \times 2l \times 3l \]
Simplifying this, we get:
\[ V = 6l^3 \]

2. **Identify the Relative Error in Length**:
The problem states that the relative percentage error in the measurement of \( l \) is 1%. This can be expressed mathematically as:
\[ \frac{\Delta l}{l} \times 100 = 1\% \]
Therefore, the relative error in \( l \) is:
\[ \frac{\Delta l}{l} = 0.01 \]

3. **Calculate the Relative Error in Volume**:
To find the relative error in volume \( V \), we use the formula for the propagation of errors. Since the volume depends on \( l \) cubed, the relative error in volume can be calculated as:
\[ \frac{\Delta V}{V} = 3 \times \frac{\Delta l}{l} \]
Substituting the value of \( \frac{\Delta l}{l} \):
\[ \frac{\Delta V}{V} = 3 \times 0.01 = 0.03 \]

4. **Convert to Percentage**:
To express this relative error as a percentage, we multiply by 100:
\[ \text{Relative percentage error in } V = 0.03 \times 100 = 3\% \]

### Final Answer:
The relative percentage error in the measurement of volume \( V \) is **3%**.

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