If error in measuring diameter of a circle is 6 %, the error in the radius of the circle would be

Answer

To solve the problem of finding the error in the radius of a circle when the error in measuring the diameter is given as 6%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Diameter and Radius**:
The diameter (D) of a circle is related to the radius (R) by the formula:
\[ D = 2R \]

2. **Identify the Error in Diameter**:
We are given that the error in measuring the diameter is 6%. This can be expressed mathematically as:
\[ \frac{\Delta D}{D} \times 100 = 6\% \]
where \(\Delta D\) is the absolute error in the diameter.

3. **Relate the Errors**:
Since the diameter is twice the radius, we can express the error in diameter in terms of the error in radius. The error in radius can be expressed as:
\[ \frac{\Delta R}{R} \times 100 \]
where \(\Delta R\) is the absolute error in the radius.

4. **Use the Relationship of Diameter and Radius**:
The relationship between the errors can be derived from the differentiation of the formula \(D = 2R\):
\[ \Delta D = 2 \Delta R \]
This means that any error in the diameter is twice the error in the radius.

5. **Set Up the Equation**:
From the previous steps, we can relate the percentage errors:
\[ \frac{\Delta D}{D} = 2 \frac{\Delta R}{R} \]
Substituting the known error in diameter:
\[ 6\% = 2 \frac{\Delta R}{R} \times 100 \]

6. **Solve for the Error in Radius**:
Rearranging the equation to find the error in radius:
\[ \frac{\Delta R}{R} \times 100 = \frac{6\%}{2} \]
\[ \frac{\Delta R}{R} \times 100 = 3\% \]

7. **Conclusion**:
Therefore, the error in the radius of the circle is:
\[ \text{Error in radius} = 3\% \]

### Final Answer:
The error in the radius of the circle would be **3%**.