Water is being filled into a water tank at 22 liters/second. The base of the tank has dimensions w = 1 meter and L = 2 meter . What is the rate of change of the height of water in the tank? (express your answer in cm/sec).

I am assuming that your tank is rectangular.

Let the water level be h metres high.

V = (100)(200)(h) = 20000h cm^3 , and 1 L = 1000 cm^3
dV/dt = 20000 dh/dt

22000 = 20000 dh/dt
dh/dt = 22000/20000 cm/sec
= 1.1 cm/sec

To find the rate of change of the height of water in the tank, we need to determine the volume of water being added and the corresponding change in height.

First, let's calculate the volume of water being added per second. Given that the water is being filled into the tank at a rate of 22 liters per second, we can convert liters to cubic meters by dividing by 1000 since 1 liter is equal to 0.001 cubic meters. Therefore, the volume of water being added per second is 22/1000 = 0.022 cubic meters.

Next, we need to find the change in height for this volume of water. We can use the formula for the volume of a rectangular tank, which is given by V = LWH, where V is the volume, L is the length, W is the width, and H is the height. Rearranging the formula to solve for the height, we have H = V/(LW).

Since the length (L) and width (W) of the tank are given as 2 meters and 1 meter, respectively, the volume of water being added per second is 0.022 cubic meters, and we can substitute these values into the formula for H:

H = 0.022 / (2 * 1)
H = 0.011 meters

Finally, we need to convert the answer to centimeters per second. Since 1 meter is equal to 100 centimeters, we can multiply the height in meters by 100 to get the rate of change in centimeters per second:

Rate of change of height = 0.011 * 100
Rate of change of height = 1.1 cm/sec

Therefore, the rate of change of the height of water in the tank is 1.1 cm/sec.