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Explanation:
To determine the minimum overall depth of the slab required to satisfy vertical deflection limits, we need to consider the following factors:

1. Deflection Criteria:
The deflection criteria for slabs is typically specified in terms of the maximum allowable deflection under service loads. Commonly used deflection limits for residential and office buildings are L/360 and L/480, respectively, where L is the clear span of the slab.

2. Calculation of Clear Span:
In this case, the slab size is given as 3 m x 3.5 m. To calculate the clear span, we need to consider the longer dimension, which is 3.5 m. Since the slab is continuous, the clear span will be the distance between supports, which is equal to the longer dimension minus twice the effective depth of the slab.

3. Calculation of Effective Depth:
The effective depth of the slab is the distance from the centroid of the reinforcement to the extreme fiber in compression. It is calculated based on the required moment capacity of the slab. However, since the question does not provide any information about the loading or the design requirements, we can assume a typical effective depth of 1/10th of the shorter dimension of the slab.

4. Calculation of Clear Span:
Using the formula for clear span calculation, we have:
Clear Span = Longer Dimension - 2 * Effective Depth

For the given slab size, the clear span will be:
Clear Span = 3.5 m - 2 * (1/10 * 3) m
Clear Span = 3.5 m - 2 * 0.3 m
Clear Span = 3.5 m - 0.6 m
Clear Span = 2.9 m

5. Calculation of Maximum Allowable Deflection:
Based on the deflection criteria, the maximum allowable deflection can be calculated as follows:
Maximum Allowable Deflection = Clear Span / Deflection Limit

For residential buildings with a deflection limit of L/360, the maximum allowable deflection will be:
Maximum Allowable Deflection = 2.9 m / 360
Maximum Allowable Deflection = 0.008 m

6. Calculation of Overall Depth:
The overall depth of the slab is the sum of the effective depth and the maximum allowable deflection. Therefore, the overall depth required to satisfy the vertical deflection limits is:
Overall Depth = Effective Depth + Maximum Allowable Deflection

For the given slab, the overall depth will be:
Overall Depth = 0.3 m + 0.008 m
Overall Depth = 0.308 m

Conclusion:
Therefore, the minimum overall depth of the slab required to satisfy vertical deflection limits is 0.308 m, which is approximately 7.5 cm. Hence, option C is the correct answer.