Assertion: The error in the measurement of radius of sphere is `0.3%`. The permissible error in its surface area is `0.6 %`.
Reason: The permissible error is calculated by the formula `(Delta A)/(A) = (4 Delta r)/( r)`.

Options

A. If both Assertion and Reason are correct and Reason is the correct explaination of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explaination of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and reason provided in the question regarding the errors in the measurement of the radius and surface area of a sphere.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the error in the measurement of the radius of a sphere is 0.3%.
- The permissible error in its surface area is stated to be 0.6%.

2. **Finding the Surface Area of a Sphere**:
- The formula for the surface area (A) of a sphere is given by:
\[ A = 4\pi r^2 \]
- Here, \( r \) is the radius of the sphere.

3. **Calculating the Percentage Error in Surface Area**:
- The percentage error in a quantity that is a function of another variable can be calculated using the formula:
\[ \text{Percentage Error in A} = n \times \text{Percentage Error in r} \]
- For the surface area \( A \), since it depends on \( r^2 \), we have:
\[ \text{Percentage Error in A} = 2 \times \text{Percentage Error in r} \]
- Given that the percentage error in the radius \( r \) is 0.3%, we can substitute this value:
\[ \text{Percentage Error in A} = 2 \times 0.3\% = 0.6\% \]

4. **Verifying the Assertion**:
- The calculated percentage error in the surface area (0.6%) matches the permissible error stated in the assertion (0.6%).
- Therefore, the assertion is **true**.

5. **Understanding the Reason**:
- The reason states that the permissible error is calculated by the formula:
\[ \frac{\Delta A}{A} = \frac{4 \Delta r}{r} \]
- However, we derived that the correct formula for the percentage error in surface area is:
\[ \frac{\Delta A}{A} = 2 \frac{\Delta r}{r} \]
- Thus, the reason provided is **false**.

6. **Conclusion**:
- The assertion is true, while the reason is false. Therefore, the correct answer is that the assertion is true but the reason is false.

### Final Answer:
- The assertion is true, but the reason is false.