andrew had 1kg block of cheese. He manages to cut the cheese into 12 slices, that are all 10cm wide, 8cm tall, and 2cm thick. If andrew had a 350g block of cheese, what volume would that block have? 

To determine the volume of the 350g block of cheese, we can start by analyzing the relationship between the mass and volume of the original 1kg block. The steps are as follows:

1. **Volume of the 1kg block**:  
   Andrew cut the 1kg block of cheese into 12 slices. Each slice is \(10 \text{ cm} \times 8 \text{ cm} \times 2 \text{ cm}\).  
   Therefore, the volume of one slice is:
   \[
   \text{Volume of one slice} = 10 \times 8 \times 2 = 160 \text{ cubic centimeters}.
   \]
   Since there are 12 slices, the total volume of the 1kg block of cheese is:
   \[
   \text{Total volume of 1kg block} = 160 \times 12 = 1920 \text{ cubic centimeters}.
   \]

2. **Density of the cheese**:  
   The mass of the 1kg block is 1000 grams, and its volume is 1920 cubic centimeters. The density \( \rho \) of the cheese can be calculated as:
   \[
   \rho = \frac{\text{Mass}}{\text{Volume}} = \frac{1000 \text{ grams}}{1920 \text{ cubic centimeters}} \approx 0.5208 \text{ grams per cubic centimeter}.
   \]

3. **Volume of the 350g block**:  
   Now, using the same density, we can find the volume of the 350g block:
   \[
   \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{350 \text{ grams}}{0.5208 \text{ grams per cubic centimeter}} \approx 672.02 \text{ cubic centimeters}.
   \]

Therefore, the volume of the 350g block of cheese is approximately **672 cubic centimeters**.

Would you like more details or have any questions?

Here are some related questions:
1. How would the volume change if the block weighed 500g?
2. What would be the dimensions of the 350g block if it had the same shape as the original slices?
3. How does the density of the cheese compare to that of other common foods?
4. If Andrew cut the 350g block into slices of the same dimensions, how many slices would he get?
5. What is the ratio of the mass of the 350g block to the 1kg block?

**Tip**: Density relates mass to volume, so once you know the density of a material, you can easily find one if you have the other.

Learn how to calculate the volume of a cheese block and its density using given dimensions and mass. Detailed step-by-step solution for a math problem involving geometry and density calculations. Suitable for Grades 7-9 students.

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