Tap A was turned on to fill a rectangular tank of 50 cm by 40 cm by 28 cm 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 minute. 6 minutes after Tap B was turned on, both taps were turned off. Find the depth of water left in the tank
For this problem, it is important to know which dimension is the height.
Is 28cm the height?
To find the depth of water left in the tank, we need to calculate the volume of water filled by Tap A and the volume drained by Tap B. Then we can subtract the volume drained from the volume filled to get the remaining water volume.
First, let's calculate the volume of water filled by Tap A:
The rate of Tap A is 6 liters per minute, and it filled water for 2 minutes. So, the volume of water filled by Tap A is 6 liters/minute * 2 minutes = 12 liters.
Since 1 liter is equal to 1000 cubic centimeters (cc), we can convert the volume to cubic centimeters (cc):
12 liters * 1000 cc/liter = 12,000 cc.
Next, let's calculate the volume drained by Tap B:
The rate of Tap B is 2 liters per minute, and it drained water for 6 minutes. So, the volume drained by Tap B is 2 liters/minute * 6 minutes = 12 liters.
Converting this to cubic centimeters (cc):
12 liters * 1000 cc/liter = 12,000 cc.
Now, let's find the remaining volume of water in the tank:
The initial volume of the tank is given as 50 cm * 40 cm * 28 cm = 56,000 cubic centimeters (cc).
The volume filled by Tap A is 12,000 cc, and the volume drained by Tap B is also 12,000 cc.
To find the remaining volume, we subtract the volume drained and the volume filled from the initial volume of the tank:
Remaining volume = Initial volume - Volume drained - Volume filled
Remaining volume = 56,000 cc - 12,000 cc - 12,000 cc = 32,000 cc.
Finally, let's find the depth of water left in the tank:
The depth is the third dimension of the rectangular tank. The dimensions are given as 50 cm by 40 cm by 28 cm.
The remaining volume is 32,000 cc.
To find the depth, divide the remaining volume by the product of the other two dimensions:
Depth = Remaining volume / (length * width)
Depth = 32,000 cc / (50 cm * 40 cm)
Depth ≈ 16 cm.