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.
ScanSolve AI Answer
Hey Young, good to see you again. Step 1: Calculate the area of the cross-section of the model pool. The cross-section is a trapezium. The lengths of the parallel sides are h_1 = 4.5 cm and h_2 = 1.5 cm. The perpendicular distance between the parallel sides (height of the trapezium) is b = 45 cm. The area of a trapezium is given by A = (1)/(2)(h_1 + h_2)b. A_m = (1)/(2)(4.5 cm + 1.5 cm) × 45 cm A_m = (1)/(2)(6 cm) × 45 cm A_m = 3 cm × 45 cm A_m = 135 cm^2 Step 2: Calculate the volume of the model pool. The length of the model pool is L_m = 30 cm. The volume of the model pool is the area of the cross-section multiplied by its length. V_m = A_m × L_m V_m = 135 cm^2 × 30 cm V_m = 4050 cm^3 Step 3: Determine the linear scale factor between the model and the actual pool. The length of the model pool is L_m = 30 cm. The length of the actual pool is L_a = 27 m. Convert this to centimeters: L_a = 27 m × 100 cmm = 2700 cm The linear scale factor k is the ratio of the actual length to the model length. k = (L_a)/(L_m) = 2700 cm30 cm k = 90 Step 4: Calculate the volume of the actual pool. The volume scale factor is k^3. k^3 = 90^3 = 729000 The volume of the actual pool V_a is the volume of the model pool multiplied by the volume scale factor. V_a = V_m × k^3 V_a = 4050 cm^3 × 729000 V_a = 2952450000 cm^3 Step 5: Convert the volume of the actual pool to litres. We know that 1000 cm^3 = 1 litre. V_a = 2952450000 cm^31000 cm^3litre V_a = 2952450 litres The capacity of the actual pool is 2952450 litres. Send me the next one 📸