An empty rectangular tank with a base are of 2400 cm2 is filled with water from two taps.one tap can fill the tank with 12 liters of waTer per minute while the other tap can do it at 3 liters per minute.
a. what will be the depth of water in the tank after both taps are turned on for 6 minutes?
B.if water leaks from the tank at 2 liters per minute for 6 minutes,what will be the depth of water in the tank?
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.
To solve these problems, we need to calculate the volume of water filled in the tank and then determine the depth of water based on the tank's base area.
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 by both taps.
The first tap fills 12 liters of water per minute, so in 6 minutes, it will fill 12 liters/min * 6 minutes = 72 liters.
The second tap fills 3 liters of water per minute, so in 6 minutes, it will fill 3 liters/min * 6 minutes = 18 liters.
Therefore, the total volume of water added by both taps is 72 liters + 18 liters = 90 liters.
Now, we can calculate the depth of the water in the tank using the formula:
Volume = Base Area * Depth
Given that the base area is 2400 cm², and the volume is 90 liters = 90000 cm³ (since 1 liter = 1000 cm³), we can rearrange the formula:
Depth = Volume / Base Area
Plugging in the values, we get:
Depth = 90000 cm³ / 2400 cm² = 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. To find the depth of water in the tank after water leaks from the tank at a rate of 2 liters per minute for 6 minutes, we need to calculate the volume of water remaining in the tank.
Water leaking at 2 liters per minute for 6 minutes will result in a total loss of 2 liters/min * 6 minutes = 12 liters.
Subtracting this loss from the previous total volume of 90 liters, we get 90 liters - 12 liters = 78 liters.
Using the same formula as before, Depth = Volume / Base Area, we can calculate the new depth of water:
Depth = 78000 cm³ / 2400 cm² = 32.5 cm
Therefore, the depth of water in the tank after water leaks at a rate of 2 liters per minute for 6 minutes would be 32.5 cm.
combined rate is 15 litres per minute.
amount in 6 min = 6(15) = 90 litres.
volume in tank = 2400h cm^3, where h is the height
= 2.4h litres, since 1000 c^3 = 1 litre
so 2.4h = 90
h = 90/2.4 cm = 37.5 cm <--- the depth of water after both taps ran for 6 minutes
b) Does the leak happen after the 90 litres are filled and the taps are turned off?
Does the leak happen right from the start?
Whichever, the leak will be 12 litres, so you will have to decide what to do with that.