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
Right Ignatius, let's go. Step 1: Identify the given dimensions and calculate the radii. The top diameter D = 28 cm, so the top radius R = (28)/(2) = 14 cm. The bottom diameter d = 21 cm, so the bottom radius r = (21)/(2) = 10.5 cm. The height of the frustum H = 20 cm. Step 2: Apply the formula for the volume of a frustum. The volume V of a frustum is given by the formula: V = (1)/(3) H (R^2 + Rr + r^2) Substitute the values: V = (1)/(3) (20) (14^2 + (14)(10.5) + 10.5^2) Step 3: Calculate the terms inside the parenthesis and the volume in cm^3. 14^2 = 196 (14)(10.5) = 147 10.5^2 = 110.25 Now, sum these values: R^2 + Rr + r^2 = 196 + 147 + 110.25 = 453.25 Substitute this back into the volume formula: V = (1)/(3) (20) (453.25) V = (9065)/(3) Using ≈ 3.14159: V ≈ (9065)/(3) × 3.14159 V ≈ 3021.6666 × 3.14159 V ≈ 9499.791 cm^3 Step 4: Convert the volume from cm^3 to litres and round to one decimal place. Since 1 litre = 1000 cm^3, divide the volume in cm^3 by 1000: V_litres = (9499.791)/(1000) litres V_litres ≈ 9.499791 litres Rounding to one decimal place: V_litres ≈ 9.5 litres The capacity of the bucket is 9.5 litres. Send me the next one 📸