https://file.aiquickdraw.com/mathbot/file/1726104617849so2i1stp.pdf

The document contains several mathematical problems focusing on expanding and simplifying expressions, volume conversions, volume calculations for cylinders and prisms, and determining capacity. Here’s a summary of the specific tasks:

### 1. **Expand and Simplify Expressions**
   - Problems:
     - \( 5(m + 3) \)
     - \( 4(d - 4) + 5 \)
     - \( 15 - 6(5y - 11) \)

### 2. **Volume Conversions**
   - Convert volumes into different units:
     - \( 20 \, \text{cm}^3 \) to mm\(^3\)
     - \( 8.3 \, \text{m}^3 \) to cm\(^3\)
     - \( 150 \, \text{mm}^3 \) to cm\(^3\)
     - \( 360,000 \, \text{m}^3 \) to km\(^3\)

### 3. **Volume of Cylinders and Prisms**
   - Use the formula \( V = A \times H \), where \( A \) is the cross-sectional area, and \( H \) is the height or depth.

### 4. **Capacity Calculation**
   - Calculate the capacity of a cylindrical coffee plunger based on the provided measurements, using the area formula for a circle \( A = \pi r^2 \).

Would you like to go through the detailed solutions for any of these problems, or is there a specific area you want to focus on? 

Here are some related questions that could help expand your understanding:

1. How do you expand and simplify algebraic expressions involving parentheses?
2. What are the key steps in converting between volume units like cm\(^3\), mm\(^3\), and m\(^3\)?
3. How do you calculate the volume of complex shapes like prisms and cylinders?
4. What are common errors to watch out for when solving volume conversion problems?
5. How can understanding the area and volume formulas help in real-world applications?

**Tip:** Always double-check your unit conversions by verifying the direction of conversion (e.g., multiplying or dividing by powers of 10).

The document contains several mathematical problems focusing on expanding and simplifying expressions, volume conversions, volume calculations for cylinders and prisms, and determining capacity.

This page covers mathematical concepts like expanding algebraic expressions, volume conversions, and the calculation of volumes for cylinders and prisms. Detailed formulas include V = πr^2h for cylinders and volume conversion techniques.

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