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: Calculate the volume of the hemispherical tank. The formula for the volume of a hemisphere is V = (2)/(3) r^3. Given radius r = 2 m and = (22)/(7). V = (2)/(3) × (22)/(7) × (2 m)^3 V = (2)/(3) × (22)/(7) × 8 m^3 V = (352)/(21) m^3 Step 2: Convert the volume from cubic meters to litres. We know that 1 m^3 = 1000 litres. V_litres = (352)/(21) × 1000 litres V_litres = (352000)/(21) litres V_litres ≈ 16761.90 litres Step 3: Calculate the total water required for the farm. The farm area is 500 m^2. Each square metre requires 50 litres of water. Total water required = Farm area × Water per square metre. Water required = 500 m^2 × 50 litres/m^2 Water required = 25000 litres Step 4: Compare the tank's capacity with the water required and state the conclusion. The tank capacity is approximately 16761.90 litres. The water required for the farm is 25000 litres. Since 16761.90 litres < 25000 litres, the full tank of water is not sufficient. Mathematical statement: V_tank < Water required (352000)/(21) litres < 25000 litres The full tank of water would not be sufficient to irrigate the farm. 3 done, 2 left today. You're making progress.