To solve this problem, let's break it down step by step.

Step 1: Calculate the area of the plates

1. Area of the 100mm plate: $\text{Area}_{100} = \pi \left( \frac{100}{2} \right)^2 = \pi (50^2) = 2500\pi \text{ mm}^2$

2. Area of a 35mm plate: $\text{Area}_{35} = \pi \left( \frac{35}{2} \right)^2 = \pi (17.5^2) \approx 306.25\pi \text{ mm}^2$

3. Total area of 40 plates: $\text{Total Area}_{35} = 40 \times \text{Area}_{35} = 40 \times 306.25\pi \approx 12250\pi \text{ mm}^2$

Step 2: Confirm the area relation

The problem states that the 35mm plates are 8 times smaller in area than the 100mm plate, so: $\text{Area}_{100} \div 8 = 2500\pi \div 8 \approx 312.5\pi \text{ mm}^2$ This does not match the area of the 35mm plates. The calculation confirms that while the areas were calculated correctly, the relation may refer to volume or a different context.

Step 3: Split the 100mm plate

You plan to split the 100mm plate 1:10, meaning you take one part of the 100mm plate and mix it with nine parts of the medium.

1. Volume from the 100mm plate: $\text{Volume from 100mm plate} = \frac{6 \text{ ml}}{10} = 0.6 \text{ ml}$

Step 4: Calculate volume for each 35mm plate

1. Total volume needed for 40 plates: $\text{Total volume for 40 plates} = 0.6 \text{ ml} \times 10 = 6 \text{ ml}$

Since we need to seed 40 plates with the 0.6 ml of the culture: $\text{Volume per 35mm plate} = \frac{0.6 \text{ ml}}{40} = 0.015 \text{ ml} = 15 \text{ µl}$

Conclusion

You will add 15 µl of the culture to each of the 35mm plates.

---

Would you like further details on any specific part of the calculations? Here are some related questions for you:

1. How do you calculate the volume based on different plate sizes?
2. What are the implications of using different volumes for transfection efficiency?
3. How do splitting ratios affect the dilution of cell cultures?
4. What is the significance of plate area in cell culture experiments?
5. Can you explain the concept of dilution factors in cell culture?

Tip: Always ensure you verify the area calculations when comparing different sizes to ensure accurate scaling for experiments.