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
Alright janetolabanji44 — let's do this. Step 1: Identify the dimensions of the frustum (bucket). The bottom radius (r_1) is 15 cm. The top radius (r_2) is 20 cm. The vertical depth (h_f) is 30 cm. We will use = (22)/(7). Step 2: Calculate the volume of water in the frustum. The formula for the volume of a frustum is V_f = (1)/(3) h_f (r_1^2 + r_1 r_2 + r_2^2). Substitute the given values: V_f = (1)/(3) × (22)/(7) × 30 × (15^2 + 15 × 20 + 20^2) V_f = (220)/(7) × (225 + 300 + 400) V_f = (220)/(7) × (925) cm^3 Step 3: Identify the dimensions of the cylindrical container. The base radius (R) of the cylinder is 20 cm. Let the depth of the water in the cylinder be H. Step 4: Equate the volume of water in the frustum to the volume of water in the cylinder. The volume of water in the cylinder is V_c = R^2 H. Since the water is poured from the frustum into the cylinder, V_c = V_f. R^2 H = (220)/(7) × 925 Substitute R = 20 and = (22)/(7): (22)/(7) × 20^2 × H = (220)/(7) × 925 (22)/(7) × 400 × H = (220)/(7) × 925 Step 5: Solve for the depth (H) of the water in the cylinder. Multiply both sides by 7 to cancel the denominators: 22 × 400 × H = 220 × 925 8800 H = 203500 Divide by 8800: H = (203500)/(8800) H = (2035)/(88) Simplify the fraction by dividing both numerator and denominator by 11: H = (185)/(8) Convert the fraction to a decimal: H = 23.125 cm The depth of the water in the cylindrical container is 23.125 cm. 23.125 cm What's next? 📸