a. To find the depth of water in the tank after both taps are turned on for 6 minutes, we need to calculate the total volume of water added and then divide it by the base area of the tank.
First, let's calculate the total volume of water added by each tap in 6 minutes:
- Tap 1: 12 liters/minute x 6 minutes = 72 liters
- Tap 2: 3 liters/minute x 6 minutes = 18 liters
Now, let's calculate the total volume of water added by both taps:
Total volume = Volume from Tap 1 + Volume from Tap 2
Total volume = 72 liters + 18 liters
Total volume = 90 liters
Next, we need to convert the volume from liters to cm3 since the base area is given in cm2. 1 liter is equivalent to 1000 cm3, so:
Total volume = 90 liters x 1000 cm3/liter
Total volume = 90,000 cm3
Finally, to find the depth of water in the tank, we divide the total volume by the base area:
Depth of water = Total volume / Base area
Depth of water = 90,000 cm3 / 2400 cm2
Depth of water = 37.5 cm
Therefore, the depth of water in the tank after both taps are turned on for 6 minutes is 37.5 cm.
b. Now, let's calculate the depth of water in the tank after water leaks from the tank for 6 minutes.
The rate of water leaking from the tank is given as 2 liters/minute. Therefore, the total volume of water leaked in 6 minutes is:
Volume leaked = 2 liters/minute x 6 minutes
Volume leaked = 12 liters
Again, let's convert the volume from liters to cm3:
Volume leaked = 12 liters x 1000 cm3/liter
Volume leaked = 12,000 cm3
Now, we need to subtract the volume leaked from the total volume added by both taps:
Total volume remaining = Total volume added - Volume leaked
Total volume remaining = 90,000 cm3 - 12,000 cm3
Total volume remaining = 78,000 cm3
Finally, we calculate the depth of water in the tank by dividing the remaining volume by the base area:
Depth of water = Total volume remaining / Base area
Depth of water = 78,000 cm3 / 2400 cm2
Depth of water = 32.5 cm
Therefore, the depth of water in the tank after water leaks from the tank for 6 minutes is 32.5 cm.