The School Garden Water Tank
A rectangular water tank at a school garden measures 2.5 m long, 1.8 m wide, and 1.2 m deep. It is filled to 80% of its capacity. A gardener uses a cylindrical bucket with a radius of 15 cm and a height of 30 cm to water the plants. He fills the bucket completely each time and empties it entirely onto the plants. After watering, the water level in the tank drops to 60% of its capacity. The gardener wants to know how many buckets of water he used and whether he can continue watering for another 10 buckets without the tank going below 25% of its capacity. (Use π ≈ 3.14; 1 m³ = 1000 L).
1. Calculate the volume of water in the tank initially and after watering. Then find the number of buckets used. Show your steps clearly.
Read the worked answer
First, find the tank's total volume: V_tank = 2.5 m × 1.8 m × 1.2 m = 5.4 m³. Convert to litres: 5.4 × 1000 = 5400 L. Initially, the tank is 80% full: 0.80 × 5400 = 4320 L. After watering, it is 60% full: 0.60 × 5400 = 3240 L. The water used = 4320 − 3240 = 1080 L. Next, find the bucket's volume: radius r = 15 cm = 0.15 m, height h = 30 cm = 0.30 m. V_bucket = π r² h = 3.14 × (0.15)² × 0.30 = 3.14 × 0.0225 × 0.30 = 3.14 × 0.00675 = 0.021195 m³. Convert to litres: 0.021195 × 1000 = 21.195 L. Number of buckets = 1080 ÷ 21.195 ≈ 50.95. Since the gardener fills the bucket completely each time, he must have used 51 buckets (the last bucket may not have been completely emptied, but the problem states he empties it entirely, so we take the integer that gives at least 1080 L; 51 buckets give 51 × 21.195 = 1080.945 L, which is slightly more than 1080 L, meaning the tank would be slightly below 60% after 51 buckets. However, the problem says the level drops to 60%, so the number of buckets is 51, with the last bucket not completely full? Actually, if he fills completely and empties entirely, the water used must be a multiple of 21.195 L. 1080 ÷ 21.195 = 50.95, not an integer. This suggests a slight inconsistency. For the purpose of the problem, we round to the nearest whole number: 51 buckets. Alternatively, if we assume the water level drop is exact, then the number of buckets must be 51, and the actual water used is 51 × 21.195 = 1080.945 L, which would make the final volume 4320 − 1080.945 = 3239.055 L, i.e., 59.98% full, which rounds to 60%. So 51 buckets is reasonable.)
2. Determine whether the gardener can use another 10 buckets without the tank going below 25% of its capacity. Justify your answer with calculations.
Read the worked answer
Current water volume after watering = 3240 L (60% of 5400 L). 25% of capacity = 0.25 × 5400 = 1350 L. Water available above the 25% mark = 3240 − 1350 = 1890 L. Water needed for 10 buckets = 10 × 21.195 = 211.95 L. Since 211.95 L < 1890 L, he can use 10 more buckets without going below 25%. In fact, he could use many more: maximum additional buckets = floor(1890 ÷ 21.195) = floor(89.17) = 89 buckets. So 10 buckets is safe. The tank will still have 3240 − 211.95 = 3028.05 L, which is about 56.1% of capacity, well above 25%.