The length of a cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier calliper having least count 0.01 cm. Given that length is 5.0 cm and radius is 2.00 cm. The percentage error in the calculated value of the volume will be

Options

A. 0.01
B. 0.02
C. 0.03
D. 0.04

Explanation

To find the percentage error in the calculated value of the volume of a cylinder, we will follow these steps:

### Step 1: Understand the formula for the volume of a cylinder
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height (length) of the cylinder.

### Step 2: Identify the given values
From the problem, we have:
- Length \( h = 5.0 \, \text{cm} \)
- Radius \( r = 2.00 \, \text{cm} \)

### Step 3: Calculate the volume of the cylinder
Substituting the values into the volume formula:
\[ V = \pi (2.00)^2 (5.0) = \pi (4.00)(5.0) = 20\pi \, \text{cm}^3 \]

### Step 4: Calculate the errors in measurements
1. **Error in length measurement**:
- Least count of the metre rod = \( 0.1 \, \text{cm} \)
- Percentage error in length:
\[ \text{Percentage error in } h = \left( \frac{0.1}{5.0} \right) \times 100 = 2\% \]

2. **Error in radius measurement**:
- Least count of the vernier caliper = \( 0.01 \, \text{cm} \)
- Percentage error in radius:
\[ \text{Percentage error in } r = \left( \frac{0.01}{2.00} \right) \times 100 = 0.5\% \]

### Step 5: Calculate the total percentage error in volume
The volume depends on both the radius and the height. The formula for the total percentage error in volume is given by:
\[ \text{Total percentage error} = \text{Percentage error in } h + 2 \times \text{Percentage error in } r \]
Substituting the values:
\[ \text{Total percentage error} = 2\% + 2 \times 0.5\% = 2\% + 1\% = 3\% \]

### Final Answer
The percentage error in the calculated value of the volume of the cylinder is **3%**.

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