A cylindrical water tank has a diameter of 140cm.To begin with it is full of water.A leak starts at the bottom so that it loses 33l of water in 1hour.How long will it take for the water level to fall by 30cm?
Are you sure you typed this correctly? It doesn't make sense for them to give you the diameter and ask about the level falling. Should 140 cm be the height?
I know right.... I also have two such questions and I'm wondering why they are not giving the height
1-cm thick layer of water has a volume of π*70^2 cm cube=15.3958L.
so, you want to know how long it takes to drain 30cm=461.874L
461.874÷33L/hr =14hr.
To determine how long it will take for the water level to fall by 30cm, we need to calculate the time required for the tank to lose 30cm of water due to the leak.
First, let's determine the volume of water that corresponds to a 30cm drop in height.
The formula for the volume of a cylinder is given by:
V = πr^2h
Where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius, and h is the height.
Since the diameter of the cylindrical water tank is 140cm, we can find the radius by dividing the diameter by 2.
So the radius (r) is 140cm / 2 = 70cm.
Now, we can calculate the volume corresponding to a 30cm drop in height:
V = π(70cm)^2 * 30cm
Using the value of π as 3.14159, this simplifies to:
V = 3.14159 * (70cm)^2 * 30cm
V = 3.14159 * 4900cm^2 * 30cm
V = 3.14159 * 147000cm^3
V ≈ 461741.84cm^3
Next, we need to find out how much water the tank loses per hour due to the leak. It is given that the tank loses 33 liters in 1 hour.
To convert liters to cubic centimeters (cm^3), we multiply by 1000 (since 1 liter = 1000 cm^3):
Therefore, the leak rate is 33 liters * 1000 = 33,000 cm^3 per hour.
Now, we can determine the time required for the tank to lose 30cm of water by dividing the volume by the leak rate:
Time = Volume / Leak Rate
Time = 461741.84cm^3 / 33000cm^3/hr
Time ≈ 13.998 hours
Therefore, it will take approximately 14 hours for the water level to fall by 30cm.