tap a was turned on to till a rectangular tank of 50cm by 40cm by 28cm with water at a rate of 6 liters per minute. after 2 minutes, tap b was turned on to drain water from the tank at a rate of 2 liters per minutes. 6 minutes after tap b was turned on, both taps were tuned off. find the depth of water left in the tank
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To find the depth of water left in the tank, we need to calculate the amount of water that was drained from the tank and subtract it from the initial amount of water.
Step 1: Calculate the initial volume of water in the tank.
The tank has dimensions of 50cm x 40cm x 28cm, so the initial volume is:
50cm x 40cm x 28cm = 56,000 cubic centimeters
Step 2: Calculate the amount of water added by tap A in 2 minutes.
Tap A adds water at a rate of 6 liters per minute.
In 2 minutes, tap A adds: 6 liters/minute x 2 minutes = 12 liters
Convert the liters to cubic centimeters: 12 liters x 1000 cubic centimeters/liter = 12,000 cubic centimeters
Step 3: Calculate the amount of water drained by tap B in 6 minutes.
Tap B drains water at a rate of 2 liters per minute.
In 6 minutes, tap B drains: 2 liters/minute x 6 minutes = 12 liters
Convert the liters to cubic centimeters: 12 liters x 1000 cubic centimeters/liter = 12,000 cubic centimeters
Step 4: Calculate the total volume of water removed.
The total volume of water removed is the sum of the water added by tap A and the water drained by tap B:
12,000 cubic centimeters + 12,000 cubic centimeters = 24,000 cubic centimeters
Step 5: Calculate the depth of water left in the tank.
To find the depth, we divide the total volume removed by the base area of the tank:
Depth = Total Volume / (Length x Width)
Depth = 24,000 cubic centimeters / (50cm x 40cm) = 24,000 cubic centimeters / 2000 square centimeters = 12 centimeters
Therefore, the depth of water left in the tank is 12 centimeters.
To find the depth of water left in the tank, we need to calculate the volume of water that entered the tank and the volume of water that drained out of the tank.
Step 1: Calculate the volume of water that entered the tank in the first 2 minutes.
The rate at which water entered the tank is 6 liters per minute. Since the time is 2 minutes, the volume is 6 liters/minute * 2 minutes = 12 liters.
Step 2: Calculate the volume of water that drained out of the tank after 6 minutes.
The rate at which water drained out of the tank is 2 liters per minute. Since the time is 6 minutes, the volume is 2 liters/minute * 6 minutes = 12 liters.
Step 3: Calculate the difference between the volume that entered and the volume that drained.
12 liters - 12 liters = 0 liters.
Step 4: Convert the volume to depth.
Since we have the dimensions of the tank, we can calculate the volume of the tank. The volume of a rectangular tank is calculated by multiplying its length, width, and height. In this case, the volume is 50 cm * 40 cm * 28 cm = 56,000 cm³.
To convert the volume to depth, we need to divide the volume by the area of the base of the tank. The area of the base is calculated by multiplying the length and width of the base. In this case, the area is 50 cm * 40 cm = 2,000 cm².
Dividing the volume of the tank (56,000 cm³) by the area of the base (2,000 cm²), we get:
56,000 cm³ ÷ 2,000 cm² = 28 cm.
Therefore, the depth of water left in the tank is 28 cm.