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To find the final cost of the shelving unit, let's calculate each component's cost and then apply the tax where applicable. Here’s the breakdown:

### 1. Cost of Sheet Metal
Given:
- 40 ft² of sheet metal needed
- Cost per ft² = $3.10

\[
\text{Sheet Metal Cost} = 40 \, \text{ft}^2 \times 3.10 = 124 \, \text{USD}
\]

### 2. Labor Cost
Given:
- $18.00/hr for labor
- 9 hours of labor

\[
\text{Labor Cost} = 18 \times 9 = 162 \, \text{USD}
\]

### 3. Paint Cost
Given:
- 2 gallons of paint
- Cost per gallon = $11

\[
\text{Paint Cost} = 2 \times 11 = 22 \, \text{USD}
\]

### 4. Total Before Tax and Delivery Fee
Sum up the costs for sheet metal, labor, and paint.

\[
\text{Subtotal Before Tax} = 124 + 162 + 22 = 308 \, \text{USD}
\]

### 5. Tax
A 15% tax applies to the subtotal.

\[
\text{Tax} = 308 \times 0.15 = 46.20 \, \text{USD}
\]

### 6. Delivery Fee
The delivery fee is $20.00, which is not taxed.

### 7. Final Cost
Add the subtotal, tax, and delivery fee.

\[
\text{Final Cost} = 308 + 46.20 + 20 = 374.20 \, \text{USD}
\]

### Answer
The final cost of the shelving unit is **$374.20**.

Would you like any further details or have any questions?

---

Here are some related questions that may expand on the calculation above:

1. How would the final cost change if the labor rate increased to $20/hour?
2. What would be the total cost if a 10% discount was applied to the sheet metal price?
3. How does the tax rate affect the total cost if it were increased to 20%?
4. If the delivery fee was also taxed, how would that impact the final cost?
5. How would the cost change if the shelving unit required 60 ft² of sheet metal instead of 40 ft²?

**Tip:** Always double-check whether each component of the cost is taxable or not before finalizing calculations.

You need 40 ft² of sheet metal to build a shelving unit. Determine the final cost of the shelving unit, given:
- $3.10/sq. ft. for sheet metal
- $18.00/hr for labour
- 9 hours of labour from start to finish
- 2 gallons of paint that cost $11/gal
- 15% tax to be charged on the above items
- A delivery fee of $20.00 that isn't taxed

This problem demonstrates how to determine the final cost of a shelving unit using 40 ft² of sheet metal. It includes calculations for labour, paint, taxes, and delivery fees, making it suitable for Grades 7-10 students learning practical applications of cost analysis.

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