The measurement of radius of a circle has error of 1%. The error in measurement of its area

Options

A. 0.01
B. 0.02
C. 0.03
D. none of these

Answer

To solve the problem of finding the error in the measurement of the area of a circle given the error in the radius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given information**:
- The error in the measurement of the radius (ΔR/R) is given as 1%. This means:
\[ \frac{\Delta R}{R} \times 100 = 1\% \]

2. **Formula for the area of a circle**:
- The area \(A\) of a circle is given by the formula:
\[ A = \pi R^2 \]

3. **Determine the relationship between the error in radius and the error in area**:
- To find the error in the area, we can use the formula for the relative error in area:
\[ \frac{\Delta A}{A} \times 100 = 2 \times \frac{\Delta R}{R} \times 100 \]
- This relationship arises because the area depends on the square of the radius.

4. **Substituting the known error**:
- We know that \(\frac{\Delta R}{R} \times 100 = 1\%\). Therefore:
\[ \frac{\Delta A}{A} \times 100 = 2 \times 1\% = 2\% \]

5. **Conclusion**:
- The error in the measurement of the area is 2%. In fraction form, this can be expressed as:
\[ \frac{\Delta A}{A} = \frac{2}{100} = 0.02 \]

Thus, the error in the measurement of the area of the circle is **2%**.