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 Samson, good to see you again. Here's how to solve this scale problem. The scale is given as 1:500. This means that 1 unit on the model represents 500 units in the actual building. a) Step 1: Find the height of the room in the actual building. The height of the room on the model is 5 cm. To find the actual height, multiply the model height by the scale factor. Actual height = Model height × Scale factor Actual height = 5 cm × 500 Actual height = 2500 cm Step 2: Convert the actual height from centimeters to meters. Since 1 m = 100 cm: Actual height in meters = 2500 cm100 cm/m Actual height in meters = 25 m The height of the room in the building is 25 m. Step 3: Find the corresponding area on the floor of the model. The actual floor area of the room is 36 m^2. For areas, the scale factor is squared. So, if the linear scale is 1:k, the area scale is 1:k^2. Here, k = 500. Area scale = (1)/(k^2) = (1)/(500^2) = (1)/(250000) To find the area on the model, divide the actual area by the square of the scale factor. Model area = Actual areaScale factor^2 Model area = 36 m^2500^2 Model area = 36 m^2250000 Model area = 0.000144 m^2 Step 4: Convert the model area from square meters to square centimeters for a more practical unit. Since 1 m = 100 cm, then 1 m^2 = (100 cm)^2 = 10000 cm^2. Model area in cm^2 = 0.000144 m^2 × 10000 cm^2/m^2 Model area in cm^2 = 1.44 cm^2 The corresponding area on the floor of the model is 1.44 cm². The height of the room in the building is 25 m. The corresponding area on the floor of the model is 1.44 cm^2. Send me the next one 📸