If the length of a cylinder is measured to be 4.28 cm with an error of 0.01 cm. The percentage error in the measured length is nearly

Options

A. `0.4%`
B. `0.5%`
C. `0.2%`
D. `0.1%`

Answer

To find the percentage error in the measured length of the cylinder, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Measured length (L) = 4.28 cm
- Error in measurement (ΔL) = 0.01 cm

2. **Use the formula for percentage error**:
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left( \frac{\Delta L}{L} \right) \times 100 \]

3. **Substitute the values into the formula**:
\[ \text{Percentage Error} = \left( \frac{0.01 \, \text{cm}}{4.28 \, \text{cm}} \right) \times 100 \]

4. **Calculate the fraction**:
\[ \frac{0.01}{4.28} \approx 0.002336 \]

5. **Multiply by 100 to find the percentage**:
\[ \text{Percentage Error} \approx 0.002336 \times 100 \approx 0.2336\% \]

6. **Round the result**:
Rounding 0.2336% gives approximately 0.23%. For practical purposes, we can say it is nearly 0.2%.

### Final Answer:
The percentage error in the measured length is nearly **0.2%**.

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