If the length of a cylinder is measured to be 50 cm with an error of 0.25 cm. The percentage error in the measured length is

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 1: Identify the given values
- Measured length of the cylinder (L) = 50 cm
- Error in measurement (ΔL) = 0.25 cm

### Step 2: Use the formula for percentage error
The formula for percentage error is given by:

\[ \text{Percentage Error} = \left( \frac{\Delta L}{L} \right) \times 100 \]

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ \text{Percentage Error} = \left( \frac{0.25 \, \text{cm}}{50 \, \text{cm}} \right) \times 100 \]

### Step 4: Calculate the fraction
Calculating the fraction:

\[ \frac{0.25}{50} = 0.005 \]

### Step 5: Multiply by 100 to find the percentage
Now, multiply by 100 to convert it to a percentage:

\[ \text{Percentage Error} = 0.005 \times 100 = 0.5\% \]

### Conclusion
The percentage error in the measured length of the cylinder is **0.5%**.

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