Let's analyze the problem step by step:

Part (a):

• Task: Draw a sketch of the pool and label the sides.
  The pool is rectangular with dimensions $9 \, \text{m}$ by $3.5 \, \text{m}$ (since $350 \, \text{cm} = 3.5 \, \text{m}$).

Part (b):

• Task: Calculate the area of the swimming pool.
  The formula for the area of a rectangle is: $\text{Area} = \text{Length} \times \text{Width}$ Substituting the given dimensions: $\text{Area} = 9 \, \text{m} \times 3.5 \, \text{m} = 31.5 \, \text{m}^2$

Part (c):

• Task: Find the perimeter and cost of fencing. The perimeter of the pool is: $\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (9 \, \text{m} + 3.5 \, \text{m}) = 2 \times 12.5 \, \text{m} = 25 \, \text{m}$ The cost of fencing is: $\text{Cost} = \text{Perimeter} \times \text{Price per meter} = 25 \, \text{m} \times 32 \, \frac{\text{\$}}{\text{m}} = 800 \, \text{\$}$

Part (d):

• Task (i): Find the area of the walking path. The walking path is $1.5 \, \text{m}$ wide around the pool. The dimensions of the pool with the path become: $\text{Total Length} = 9 \, \text{m} + 2 \times 1.5 \, \text{m} = 12 \, \text{m}, \quad \text{Total Width} = 3.5 \, \text{m} + 2 \times 1.5 \, \text{m} = 6.5 \, \text{m}.$ The area of the pool with the walking path is: $\text{Area (Pool + Path)} = \text{Total Length} \times \text{Total Width} = 12 \, \text{m} \times 6.5 \, \text{m} = 78 \, \text{m}^2$ The area of the walking path alone is: $\text{Area (Path)} = \text{Area (Pool + Path)} - \text{Area (Pool)} = 78 \, \text{m}^2 - 31.5 \, \text{m}^2 = 46.5 \, \text{m}^2$

• Task (ii): Determine the cost of paving the path. The cost of paving is: $\text{Cost} = \text{Area (Path)} \times \text{Price per square meter} = 46.5 \, \text{m}^2 \times 74 \, \frac{\text{\$}}{\text{m}^2} = 3441 \, \text{\$}$

Let me know if you'd like detailed steps or sketches of the pool and path. Would you like to review a summary of this? Here are five related questions to explore further:

1. How would the calculations change if the pool width increased by 1 meter?
2. What is the total land area required to accommodate both the pool and path?
3. How would costs vary if fencing was priced differently, e.g., $40/m?
4. Can you calculate the walking path area for irregularly shaped pools?
5. What factors should be considered for material durability when paving the path?

Tip: Always double-check unit conversions (e.g., cm to m) to ensure accuracy in area and perimeter calculations!