This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the calculations for the swimming pool: a) Calculate how many litres of water will fill the pool if 1000 cm^3 = 1 L. Step 1: Identify the dimensions of the cylindrical pool. The diameter (D) is 4.2 m. The radius (r) is half of the diameter: r = (D)/(2) = 4.2 m2 = 2.1 m The height (h) is 1.7 m. Step 2: Calculate the volume of the cylinder in cubic meters. The formula for the volume of a cylinder is V = r^2 h. V = (2.1 m)^2 (1.7 m) V = (4.41 m^2) (1.7 m) V = 7.497 m^3 Using ≈ 3.14159: V ≈ 7.497 × 3.14159 m^3 V ≈ 23.5547 m^3 Step 3: Convert the volume from cubic meters to cubic centimeters. We know that 1 m = 100 cm, so 1 m^3 = (100 cm)^3 = 1,000,000 cm^3. V in cm^3 = 23.5547 m^3 × 1,000,000 cm^3m^3 V ≈ 23,554,700 cm^3 Step 4: Convert the volume from cubic centimeters to litres. Given that 1000 cm^3 = 1 L. V in L = 23,554,700 cm^31000 cm^3L V ≈ 23,554.7 L The volume of water that will fill the pool is 23554.7 L. b) How many square metres of tiles are needed to tile the inside of the pool? Step 1: Determine the areas to be tiled. The inside of the pool consists of the circular base and the lateral (curved) surface area. Area of the base (A_base) = r^2 Lateral surface area (A_lateral) = 2 r h Total area (A_total) = A_base + A_lateral Step 2: Calculate the area of the base. A_base = (2.1 m)^2 A_base = 4.41 m^2 A_base ≈ 4.41 × 3.14159 m^2 A_base ≈ 13.854 m^2 Step 3: Calculate the lateral surface area. A_lateral = 2 (2.1 m) (1.7 m) A_lateral = 7.14 m^2 A_lateral ≈ 7.14 × 3.14159 m^2 A_lateral ≈ 22.431 m^2 Step 4: Calculate the total area for tiling. A_total = A_base + A_lateral A_total = 13.854 m^2 + 22.431 m^2 A_total = 36.285 m^2 Rounding to two decimal places: The total area of tiles needed is 36.29 m^2. c) If the tiles cost R54,99/m^2, calculate the cost of tiles for the pool. Step 1: Use the total area calculated in part (b) and the given cost per square meter. Total area = 36.285 m^2 Cost per square meter = R54.99/m^2 Step 2: Calculate the total cost. Cost = Total area × Cost per square meter Cost = 36.285 m^2 × R54.99/m^2 Cost ≈ R1995.25215 Rounding to two decimal places for currency: The cost of tiles for the pool is R1995.25. 3 done, 2 left today. You're making progress.