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's the solution for question 8: Step 1: Understand the relationship between surface area ratio and length ratio. For similar solids, if the ratio of their corresponding lengths is k, then the ratio of their surface areas is k^2. Given the ratio of surface areas of the smaller solid to the bigger solid is 4:25. Let k be the ratio of corresponding lengths (smaller to bigger). k^2 = (4)/(25) To find k, take the square root of both sides: k = sqrt((4)/(25)) = sqrt(4)sqrt(25) = (2)/(5) Step 2: Understand the relationship between length ratio and volume ratio. For similar solids, if the ratio of their corresponding lengths is k, then the ratio of their volumes is k^3. Using the value of k from Step 1, the ratio of the volumes (smaller to bigger) is: k^3 = ((2)/(5))^3 = (2^3)/(5^3) = (8)/(125) Step 3: Calculate the volume of the smaller solid. Let V_S be the volume of the smaller solid and V_B be the volume of the bigger solid. We have the ratio (V_S)/(V_B) = (8)/(125). Given that the volume of the bigger solid V_B = 62.5 cm^3. Now, substitute the value of V_B into the ratio equation: (V_S)/(62.5 cm)^3 = (8)/(125) V_S = (8)/(125) × 62.5 cm^3 V_S = 8 × (62.5)/(125) cm^3 V_S = 8 × 0.5 cm^3 V_S = 4 cm^3 Send me the next one 📸