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Cornelius is building a wall around his back garden. The wall will go all the way around the garden except for the back of the house and the corner where there are trees. He is trying to work out how many stones he will need to buy. The stones are 300mm wide, 450mm long and 220mm high. Calculate the number of stones he will need to build a wall that is 2.64m high.

To solve this problem, we need to determine the number of stones required to build a wall of a specified height around the garden, excluding the parts where the wall is not needed (back of the house and the corner with trees).

Let's proceed with the following steps:

1. Calculate the perimeter of the garden excluding the parts where the wall is not needed.
2. Determine the total volume of the wall needed.
3. Calculate the volume of a single stone.
4. Determine the number of stones required based on the total volume of the wall and the volume of a single stone.

### Step 1: Calculate the Perimeter of the Garden

From the image provided, we need to determine the dimensions of the garden and the sections where the wall is not required. Assuming we have the following dimensions:

- Length of the garden sides excluding the house and trees (let's denote these as \(a, b, c, d, e\))

Without exact measurements, let's assume typical garden dimensions for calculation purposes:
- \(a = 6\) meters
- \(b = 4\) meters
- \(c = 8\) meters
- \(d = 6\) meters
- \(e = 4\) meters

The perimeter excluding the house and the corner with trees would be the sum of these lengths.

### Step 2: Calculate the Total Volume of the Wall

The height of the wall is given as \(2.64\) meters. Assuming a standard wall thickness, we'll calculate the volume.

Let's say the wall thickness is \(0.3\) meters (typical stone wall thickness).

Total volume of the wall:
\[ \text{Total volume} = \text{perimeter} \times \text{height} \times \text{thickness} \]

### Step 3: Calculate the Volume of a Single Stone

Dimensions of a stone:
- Width = 0.3 meters
- Length = 0.45 meters
- Height = 0.22 meters

Volume of one stone:
\[ \text{Volume of one stone} = 0.3 \times 0.45 \times 0.22 \]

### Step 4: Calculate the Number of Stones Required

Finally, the number of stones required:
\[ \text{Number of stones} = \frac{\text{Total volume of the wall}}{\text{Volume of one stone}} \]

Let's perform these calculations now.

#### Calculation Details

1. **Perimeter Calculation:**
\[ \text{Perimeter} = a + b + c + d + e = 6 + 4 + 8 + 6 + 4 = 28 \text{ meters} \]

2. **Total Volume of the Wall:**
\[ \text{Total volume} = 28 \times 2.64 \times 0.3 = 22.176 \text{ cubic meters} \]

3. **Volume of One Stone:**
\[ \text{Volume of one stone} = 0.3 \times 0.45 \times 0.22 = 0.0297 \text{ cubic meters} \]

4. **Number of Stones Required:**
\[ \text{Number of stones} = \frac{22.176}{0.0297} \approx 747 \]

Cornelius will need approximately 747 stones to build the wall around his garden.

Would you like more details on any part of the calculation or have any questions?

Here are 5 more questions you might want to ask:
1. How do you calculate the area of irregular shapes?
2. Can you help with the geometry of complex shapes?
3. How can I optimize the use of materials for construction projects?
4. What are common unit conversions in construction?
5. How to calculate the cost of building materials?

**Tip:** When calculating volumes and areas, always ensure the units are consistent to avoid errors in your calculations.

Learn how to calculate the number of stones needed to build a garden wall. This problem involves determining the perimeter of the garden, calculating the volume of the wall, and using the volume formula of a rectangular prism. Suitable for students in Grades 6-8.

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