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
Here are the solutions to the practice exercises: 1. Two similar cones have volumes of 324 cm^3 and 96 cm^3 respectively. Determine their volume scale factor. Step 1: Identify the given volumes. Let V_1 = 324 cm^3 and V_2 = 96 cm^3. Step 2: Calculate the ratio of the volumes. The volume scale factor is the ratio of the volumes. Volume scale factor = (V_1)/(V_2) = (324)/(96) Step 3: Simplify the ratio. (324)/(96) = (162)/(48) = (81)/(24) = (27)/(8) The volume scale factor is (27)/(8). 2. A scouts tent in the shape of a triangular prism has a cross-sectional area of 10 m^2 and a length of 5 m. Another similar tent has a cross-sectional area of 40 m^2 and length 10 m. Determine the volume scale factor. Step 1: Identify the given dimensions for the two similar tents. For Tent 1: L_1 = 5 m. For Tent 2: L_2 = 10 m. Step 2: Determine the linear scale factor (k). The linear scale factor is the ratio of corresponding lengths. k = (L_2)/(L_1) = 10 m5 m = 2 Step 3: Calculate the volume scale factor. The volume scale factor is the cube of the linear scale factor (k^3). Volume scale factor = k^3 = (2)^3 = 8 The volume scale factor is 8. 3. A model of a cylindrical water tank has a radius of 10.5 cm and a height of 15 cm. Its actual radius is 210 cm. Determine: a. the volume of the actual water tank. (Take = 3.142) b. the volume scale factor. a) The volume of the actual water tank. Step 1: Identify the dimensions of the model and the actual tank. Model: r_m = 10.5 cm, h_m = 15 cm. Actual: $r_a =