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
Actual: r_a = 210 cm. a) The volume of the actual water tank. Step 2: Calculate the linear scale factor (k). The linear scale factor is the ratio of corresponding lengths. k = Actual radiusModel radius = (r_a)/(r_m) = 210 cm10.5 cm = 20 Step 3: Calculate the actual height (h_a). Since the tanks are similar, the ratio of heights is equal to the linear scale factor. h_a = k × h_m = 20 × 15 cm = 300 cm Step 4: Calculate the volume of the actual water tank (V_a). The formula for the volume of a cylinder is V = r^2 h. V_a = r_a^2 h_a V_a = 3.142 × (210 cm)^2 × 300 cm V_a = 3.142 × 44100 cm^2 × 300 cm V_a = 3.142 × 13230000 cm^3 V_a = 41569860 cm^3 The volume of the actual water tank is 41569860 cm^3. b) The volume scale factor. Step 1: Use the linear scale factor (k) found in part (a). The volume scale factor is the cube of the linear scale factor. Volume scale factor = k^3 Volume scale factor = (20)^3 Volume scale factor = 8000 The volume scale factor is 8000. 3 done, 2 left today. You're making progress.