If error in measuring diameter of a circle is 4 %, the error in the radius of the circle would be

Options

A. 0.02
B. 0.08
C. 0.04
D. 0.01

Explanation

To solve the problem of finding the error in the radius of a circle given the error in measuring the diameter, 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 Given Error in Diameter:**
The problem states that the error in measuring the diameter is 4%. This can be expressed mathematically as:
\[ \frac{\Delta D}{D} \times 100 = 4 \]
where \( \Delta D \) is the absolute error in diameter.

3. **Express the Error in Terms of Radius:**
Since \( D = 2R \), we can express the error in diameter in terms of the error in radius. The relationship between the errors is given by:
\[ \frac{\Delta D}{D} = \frac{\Delta R}{R} \]
Therefore, we can write:
\[ \frac{\Delta D}{D} = \frac{\Delta R}{2R} \]

4. **Substituting the Known Error:**
From the previous step, we can substitute the known error in diameter:
\[ \frac{\Delta R}{2R} = \frac{4}{100} \]

5. **Solving for the Error in Radius:**
To find the percentage error in the radius, we can rearrange the equation:
\[ \Delta R = \frac{4}{100} \times 2R \]
This simplifies to:
\[ \Delta R = \frac{8}{100}R \]
Now, we can express the percentage error in radius:
\[ \frac{\Delta R}{R} \times 100 = \frac{8}{100} \times 100 = 8\% \]

6. **Conclusion:**
Therefore, the error in the radius of the circle is 8%.

### Final Answer:
The error in the radius of the circle would be **8%**.