This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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Here is the solution to your question in English: a) Volume of air Step 1: Convert all dimensions to meters. The diameter of the first and second sections: D_1 = 500 mm = 0.5 m. So, the radius r_1 = 0.25 m. The diameter of the third section: D_2 = 800 mm = 0.8 m. So, the radius r_2 = 0.4 m. The length of the first section (horizontal): L_1 = 2 m. The length of the second section (vertical, upper): L_2 = 1.5 m. The length of the third section (vertical, lower): L_3 = 1.5 m. Step 2: Calculate the volume of air in each cylindrical section using the formula V = r^2 L. Section 1 (horizontal): V_1 = (0.25 m)^2 (2 m) = 0.125 m^3 Section 2 (vertical, upper): V_2 = (0.25 m)^2 (1.5 m) = 0.09375 m^3 Section 3 (vertical, lower): V_3 = (0.4 m)^2 (1.5 m) = 0.24 m^3 Step 3: Calculate the total volume of air. V_total = V_1 + V_2 + V_3 = (0.125 + 0.09375 + 0.24) m^3 = 0.45875 m^3 Using ≈ 3.14159: V_total ≈ 0.45875 × 3.14159 m^3 ≈ 1.4412 m^3 Step 4: Convert the total volume to liters (1 m^3 = 1000 litres). V_total = 1.4412 m^3 × 1000 litres/m^3 = 1441.2 litres Rounding to the nearest liter: a) 1441 litres Note: The provided answer for (a) is 1458 litres. This difference (16.8 litres) likely accounts for the volume of the bends, which are not explicitly dimensioned in the diagram. My calculation is based on the straight cylindrical sections only. b) Cross-sectional area of the sheet metal Step 1: Calculate the surface area of each cylindrical section (excluding the ends) using the formula A = 2 r L. Section 1 (horizontal): A_1 = 2 (0.25 m) (2 m) = 1 m^2 Section 2 (vertical, upper): A_2 = 2 (0.25 m) (1.5 m) = 0.75 m^2 Section 3 (vertical, lower): A_3 = 2 (0.4 m) (1.5 m) = 1.2 m^2 Step 2: Calculate the total base area of the sheet metal required (without waste). A_base = A_1 + A_2 + A_3 = (1 + 0.75 + 1.2) m^2 = 2.95 m^2 A_base ≈ 2.95 × 3.14159 m^2 ≈ 9.2677 m^2 Step 3: Add 25% for waste. A_total = A_base × (1 + 0.25) = 9.2677 m^2 × 1.25 ≈ 11.5846 m^2 Rounding to two decimal places: b) 11.58 m^2 Note: The provided answer for (b) is 9.77 m^2. If this value represents the area without waste, then the total area including 25% waste would be 9.77 m^2 × 1.25 = 12.2125 m^2. My direct calculation for the base area is 9.2677 m^2, which is different from 9.77 m^2. This discrepancy likely arises from how the surface area of the bends is calculated or approximated. c) Cost of the sheet metal Step 1: Calculate the cost using the total area of sheet metal required (including waste) and the cost per square meter. Using my calculated total area from (b): Cost = 11.5846 m^2 × £11.50/m^2 ≈ £133.22 Rounding to two decimal places: c) £133.22 Note: If we use the provided answer for (b) as the base area (9.77 m^2) and then add 25% waste, the total area would be 9.77 m^2 × 1.25 = 12.2125 m^2. In this case, the cost would be 12.2125 m^2 × £11.50/m^2 = £140.44375 ≈ £140.45, which matches the provided answer for (c). That's 2 down. 3 left today — send the next one.