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 when the error in measuring the diameter is given as 4%, we can follow these steps:

### Step 1: Understand the relationship between diameter and radius
The radius (r) of a circle is half of the diameter (d). This can be expressed mathematically as:
\[ r = \frac{d}{2} \]

### Step 2: Determine the error in diameter
The problem states that the error in measuring the diameter is 4%. This means that if the diameter is measured as \( d \), the error can be expressed as:
\[ \text{Error in diameter} = 4\% \text{ of } d = \frac{4}{100} \times d = 0.04d \]

### Step 3: Calculate the error in radius
Since the radius is half of the diameter, we can find the error in the radius by considering how the change in diameter affects the radius. The change in radius (\( \Delta r \)) can be calculated as:
\[ \Delta r = \frac{\Delta d}{2} \]
Where \( \Delta d \) is the error in diameter.

Substituting the error in diameter:
\[ \Delta r = \frac{0.04d}{2} = 0.02d \]

### Step 4: Determine the percentage error in radius
To find the percentage error in the radius, we need to express the change in radius as a percentage of the radius itself. The radius can be expressed in terms of diameter:
\[ r = \frac{d}{2} \]

Now, the percentage error in radius is given by:
\[ \text{Percentage error in radius} = \left( \frac{\Delta r}{r} \right) \times 100 \]

Substituting the values:
\[ \text{Percentage error in radius} = \left( \frac{0.02d}{\frac{d}{2}} \right) \times 100 \]
\[ = \left( \frac{0.02d \times 2}{d} \right) \times 100 \]
\[ = 0.04 \times 100 = 4\% \]

### Conclusion
Thus, the error in the radius of the circle is also 4%.

### Final Answer
The error in the radius of the circle is 4%.

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