a cubical water tank is filled by tap water at the rate of 1.4liters per second. find the length of the tank in centimeters if the tank if completely filled in 28minutes
28 min = 1680 seconds
1.4 L/s * 1680s = 2352 L = 2352000 cm^3
so, the side of the cube is 133 cm
To find the length of the tank, we need to know the volume of the tank. Since we are given the rate at which water is filled in the tank, we can use this rate to calculate the volume and then find the length of the tank.
Given:
Rate of filling the tank = 1.4 liters per second
Time taken to fill the tank completely = 28 minutes
First, let's convert the time taken to seconds:
28 minutes = 28 x 60 = 1680 seconds
To find the volume of the tank, we need to multiply the rate of filling by the time taken:
Volume = Rate × Time
Volume = 1.4 liters/second × 1680 seconds
Volume = 2352 liters
Since the tank is a cube, the volume can also be calculated by multiplying the length of one side by itself three times:
Volume = length × length × length
2352 = length × length × length
To find the length, we can take the cubic root of both sides:
length = cubic root of 2352
Now, let's calculate the length of the tank:
length ≈ ∛(2352)
length ≈ 13.74
Therefore, the length of the tank is approximately 13.74 centimeters.
To find the length of the tank, we first need to calculate the total volume of water that flows into it. Since the water is flowing at a rate of 1.4 liters per second, we can find the total volume of water in liters by multiplying the flow rate by the time.
First, let's convert the time from minutes to seconds.
28 minutes × 60 seconds/minute = 1680 seconds
Next, multiply the flow rate by the time to find the total volume of water.
1.4 liters/second × 1680 seconds = 2352 liters
Since the tank is cubical, all sides have the same length. Let's call the length of each side of the tank "s". The volume of a cube is given by s^3, so we can equate this to the total volume of water.
s^3 = 2352 liters
To find the length of each side, we need to solve for s. Taking the cube root of both sides will give us the length of each side in liters.
s = ∛2352 liters ≈ 13.86 liters
Finally, the length of each side of the tank in centimeters can be found by converting liters to cubic centimeters. Since 1 liter is equal to 1000 cubic centimeters, we can multiply the length in liters by 1000.
Length = 13.86 liters × 1000 cubic centimeters/liter = 13,860 centimeters
Therefore, the length of the tank is approximately 13,860 centimeters.