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
b) Step 1: Determine the volume scale factor. The linear scale is 1:500. For volumes, the scale factor is cubed. So, if the linear scale is 1:k, the volume scale is 1:k^3. Here, k = 500. Volume scale factor = 500^3 Volume scale factor = 500 × 500 × 500 Volume scale factor = 125,000,000 The volume scale is 1:125,000,000. Step 2: Calculate the volume of the room in the model. The actual volume of the room is 120 m^3. To find the model volume, divide the actual volume by the volume scale factor. Model volume = Actual volumeVolume scale factor Model volume = 120 m^3125,000,000 Model volume = 0.00000096 m^3 Step 3: Convert the model volume from cubic meters to cubic centimeters. Since 1 m = 100 cm, then 1 m^3 = (100 cm)^3 = 1,000,000 cm^3. Model volume in cm^3 = 0.00000096 m^3 × 1,000,000 cm^3/m^3 Model volume in cm^3 = 0.96 cm^3 The corresponding volume of the model is 0.96 cm³. The corresponding volume of the model in cm^3 is 0.96 cm^3. That's 2 down. 3 left today — send the next one.