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 calculations for the volume of water and the number of buckets. d) The volume of water required to fill the tank in litres. Step 1: Convert the tank dimensions from meters to centimeters. Tank radius (R_T) = 1.4 m = 1.4 × 100 cm = 140 cm Tank height (H_T) = 2.4 m = 2.4 × 100 cm = 240 cm Step 2: Calculate the volume of the cylindrical tank in cubic centimeters. The formula for the volume of a cylinder is V = R^2 H. V_T = (140 cm)^2 (240 cm) V_T = (19600 cm^2) (240 cm) V_T = 4704000 cm^3 Step 3: Convert the volume from cubic centimeters to litres. Since 1 litre = 1000 cm^3: V_T (litres) = 4704000 cm^31000 cm^3/litre V_T (litres) = 4704 litres Using ≈ 3.14159: V_T (litres) ≈ 4704 × 3.14159 litres V_T (litres) ≈ 14778.1056 litres Step 4: Round the answer to one decimal place. V_T ≈ 14778.1 litres The volume of water required to fill the tank is 14778.1 litres. e) Calculate the number of buckets that must be drawn to fill the tank. Step 1: Calculate the volume of one bucket (frustum) in cubic centimeters. The formula for the volume of a frustum is V_f = (1)/(3) h_f (R^2 + Rr + r^2). Bucket depth (h_f) = 12 cm Top radius (R) = 10 cm Bottom radius (r) = 6 cm V_B = (1)/(3) (12 cm) ((10 cm)^2 + (10 cm)(6 cm) + (6 cm)^2) V_B = 4 cm (100 cm^2 + 60 cm^2 + 36 cm^2) V_B = 4 cm (196 cm^2) V_B = 784 cm^3 Step 2: Calculate the number of buckets required by dividing the total tank volume by the volume of one bucket. N = Volume of tankVolume of one bucket N = 4704000 cm^3784 cm^3 The terms cancel out: N = (4704000)/(784) N = 6000 The number of buckets that must be drawn to fill the tank is 6000. That's 2 down. 3 left today — send the next one.