The error in the measurement of length and radius of a cylinder are 1% and 2% respectively. The maximum percentage of error in its volume is

Options

A. 0.03
B. 0.05
C. 0.06
D. 0.1

Answer

To find the maximum percentage error in the volume of a cylinder given the percentage errors in the measurements of its length and radius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Volume Formula**:
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).

2. **Identify the Errors**:
The problem states that:
- The error in the measurement of length (height) \( h \) is 1%.
- The error in the measurement of radius \( r \) is 2%.

3. **Calculate the Percentage Error in Volume**:
The formula for the percentage error in volume \( V \) based on the errors in radius and height is:
\[ \text{Percentage Error in } V = 2 \times \text{Percentage Error in } r + \text{Percentage Error in } h \]
Here, the factor of 2 for the radius is because the radius is squared in the volume formula.

4. **Substitute the Values**:
Substitute the given percentage errors into the formula:
\[ \text{Percentage Error in } V = 2 \times 2\% + 1\% \]
\[ = 4\% + 1\% \]
\[ = 5\% \]

5. **Final Result**:
Therefore, the maximum percentage error in the volume of the cylinder is:
\[ \text{Maximum Percentage Error in Volume} = 5\% \]