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We are tasked with calculating the total cost of the edging for a pond shaped as a sector of a circle.

### Given:
- The sector has a central angle of \(210^\circ\) and two radii of 3.5 meters.
- The edging needs to be applied to the perimeter of the pond, which consists of the arc and the two straight edges (the radii).
- Edging is sold in lengths of 1.75 meters, with each length costing £2.99.

### Step-by-Step Solution:

1. **Calculate the length of the arc**:
   The formula for the arc length of a circle is:
   \[
   L = 2 \pi r \times \left(\frac{\theta}{360}\right)
   \]
   where:
   - \(r = 3.5 \, \text{m}\) (radius),
   - \(\theta = 210^\circ\) (central angle in degrees),
   - \(\pi \approx 3.1416\).

   Substituting the values:
   \[
   L = 2 \times 3.1416 \times 3.5 \times \left(\frac{210}{360}\right)
   \]
   \[
   L \approx 12.5664 \times 0.5833 = 7.33 \, \text{meters}
   \]

2. **Calculate the total perimeter**:
   The total perimeter includes the arc length and the two radii:
   \[
   \text{Perimeter} = \text{Arc length} + 2 \times \text{Radius}
   \]
   Substituting:
   \[
   \text{Perimeter} = 7.33 + 2 \times 3.5 = 7.33 + 7 = 14.33 \, \text{meters}
   \]

3. **Determine the number of edging pieces required**:
   Each piece of edging is 1.75 meters long. The total number of pieces required is:
   \[
   \text{Number of pieces} = \frac{\text{Total perimeter}}{\text{Length of one piece}}
   \]
   Substituting:
   \[
   \text{Number of pieces} = \frac{14.33}{1.75} \approx 8.19
   \]
   Since Toby cannot buy a fraction of a piece, he will need to buy 9 pieces.

4. **Calculate the total cost**:
   Each piece of edging costs £2.99. Therefore, the total cost is:
   \[
   \text{Total cost} = 9 \times 2.99 = 26.91 \, \text{pounds}
   \]

### Final Answer:
The total cost of edging Toby needs to buy is **£26.91**.

---

Would you like further clarification or details on any of the steps? Here are some related questions to expand on this problem:

1. How is the arc length formula derived from the circumference of a circle?
2. What would happen if the radius was doubled? How would it affect the cost?
3. Could you calculate the total perimeter for a different angle, such as 180°?
4. How would the cost change if the edging was sold in lengths of 2 meters instead of 1.75 meters?
5. Can you explain how the central angle affects the perimeter of the sector?

**Tip**: Always remember to round up when dealing with real-world problems that involve buying whole units, like pieces of edging.

The pond is in the shape of a sector of a circle. Toby is going to put edging on the perimeter of the pond. Edging is sold in lengths of 1.75 meters. Each length of edging costs £2.99. Work out the total cost of edging Toby needs to buy.

Find out how to calculate the total cost of edging needed for a sector-shaped pond with a central angle of 210° and radius of 3.5 meters. The solution includes arc length calculation, perimeter of the sector, and the final cost. Suitable for geometry students in Grades 8-10.

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