You are setting up plates for transfection.  You begin with 1 plate (100mm in
diameter) and have to seed 40 plates (35mm in diameter and 8 times smaller in area than the 100mm plates).  If you split the 100mm plate 1:10, how much volume will you add to each of the 35mm plates given that your starter culture is 6 mls?  Show your calculations.




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.

You are setting up plates for transfection. You begin with 1 plate (100mm in diameter) and have to seed 40 plates (35mm in diameter and 8 times smaller in area than the 100mm plates). If you split the 100mm plate 1:10, how much volume will you add to each of the 35mm plates given that your starter culture is 6 mls? Show your calculations.

Explore the step-by-step solution for calculating the volume to add to 35mm plates when starting from a 100mm plate culture. This problem involves geometry and proportions, yielding a volume of 15 µl for each plate.

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