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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. The wall is 2.64m high. Cornelius needs to have a concrete foundation for his stone wall. This will be 500mm deep. Cornelius will purchase barrowed concrete.

Work out how much this will cost him by following the price guide.

To determine the total cost of the concrete for Cornelius's wall foundation, we need to perform the following calculations:

1. **Calculate the perimeter of the garden where the wall will be built.**
2. **Calculate the volume of concrete needed for the foundation.**
3. **Determine the cost of the required concrete.**

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

From the diagram provided, we need to find the lengths of all the segments that will have the wall:

- The front (Red brick): 9.6 m
- The right side (House edge): 10 m
- The top (Opposite to the house): 12 m
- The left side (Trees): 8.8 m

Since Cornelius is not building the wall where there are trees or where the house is located, we exclude those parts:

\[ \text{Total length of wall} = 9.6 + 10 + 12 = 31.6 \, \text{m} \]

### Step 2: Calculate the Volume of Concrete Needed for the Foundation

The foundation is 500mm (0.5m) deep. The width of the foundation should ideally match the width of the wall or slightly more. Let's assume it matches the width of a stone, which is 300mm (0.3m).

**Volume calculation:**

\[ \text{Volume} = \text{length} \times \text{width} \times \text{depth} \]

For the foundation:

\[ \text{Volume} = 31.6 \, \text{m} \times 0.3 \, \text{m} \times 0.5 \, \text{m} \]
\[ \text{Volume} = 4.74 \, \text{m}^3 \]

### Step 3: Determine the Cost of Concrete

Cornelius will purchase barrowed concrete. According to the price list:

- For \(1 \, \text{m}^3\): £125
- For \(2 \, \text{m}^3\): £105
- For \(3 \, \text{m}^3\): £100
- For \(4 \, \text{m}^3\): £99
- For \(5 \, \text{m}^3\): £90

Since Cornelius needs 4.74 \(m^3\), he should consider purchasing 5 \(m^3\).

**Cost calculation:**

\[ \text{Cost} = 5 \times £90 = £450 \]

### Total Cost

The total cost for the concrete foundation is £450.

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Would you like further details or have any questions?

Here are some questions you might consider:

1. How many stones are needed for the wall?
2. What is the total cost of stones required for the wall?
3. What is the exact height of the wall in terms of the stone's height?
4. How long will it take to build the wall?
5. What are the labor costs associated with building the wall?

**Tip:** Always verify the dimensions and calculations for accuracy before purchasing materials.

Learn how to calculate the cost of concrete for Cornelius's garden wall foundation. This problem involves geometry, volume calculation, and cost estimation based on specific dimensions and price guide. Suitable for Grades 6-8.

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