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
Step 1: Identify the given values. The frustum has: • Top radius, r_1 = US = 3 cm • Bottom radius, r_2 = RV = 8 cm • Height of the frustum, h = UV = 10 cm • Use = 3.142 Step 2: Write the formula for the volume of a frustum. The volume of a frustum is given by the formula: V = (1)/(3) h (r_1^2 + r_1 r_2 + r_2^2) Step 3: Substitute the values into the formula. V = (1)/(3) × 3.142 × 10 × (3^2 + (3)(8) + 8^2) Step 4: Calculate the terms inside the parenthesis. V = (1)/(3) × 3.142 × 10 × (9 + 24 + 64) V = (1)/(3) × 3.142 × 10 × (97) Step 5: Perform the multiplication. V = (1)/(3) × 31.42 × 97 V = (3047.74)/(3) V = 1015.9133... Step 6: Round the answer to a reasonable number of decimal places. V ≈ 1015.91 cm^3 The volume of the frustum is: 1015.91 cm^3 That's 2 down. 3 left today — send the next one.