A water tank has the shape of a rectangular prism of base 50 cm2. This tank is being filled at the rate of 12 liters per minutes. Find the rate at which the height of the water in the water tank increases; express your answer in millimeters per second.

I have no idea how to do this...Can anyone help me?

Of course! I'd be happy to help you solve this problem step by step.

First, let's gather the given information:
- The water tank has the shape of a rectangular prism.
- The base of the tank has an area of 50 cm^2.
- The tank is being filled at a rate of 12 liters per minute.

To find the rate at which the height of the water in the tank increases, we need to consider the relationship between the volume, area, and height of the tank.

The volume (V) of a rectangular prism can be calculated by multiplying the base area (A) by the height (h):
V = A * h

Next, we need to convert the given fill rate of 12 liters per minute to cubic centimeters per second (since we want to express the answer in millimeters per second).

Since 1 liter is equal to 1000 cubic centimeters, we can calculate the fill rate in cubic centimeters per second as follows:
Fill rate (in cm^3/s) = (12 liters/min) * (1000 cm^3 / 1 liter) * (1 min / 60 s)

Now that we have the fill rate in cubic centimeters per second, we can use it to find the rate at which the height of the water in the tank increases.

Let's assume that the height of the water in the tank is increasing at a rate of dh/dt (in cm/s). We need to find this rate.

Using the formula for the volume (V), we can differentiate both sides of the equation with respect to time (t):
dV/dt = d(A * h)/dt

Since the base area (A) is constant and the volume (V) is increasing at a constant rate, the derivative of A with respect to t is zero. Therefore, the equation simplifies to:

dV/dt = A * (dh/dt)

Now, let's substitute the values we have:
Fill rate (in cm^3/s) = A * (dh/dt)

Since the base area (A) is given as 50 cm^2, we can replace A with 50:
Fill rate = 50 * (dh/dt)

Solving for dh/dt, we get:
dh/dt = Fill rate / 50

Now, we can substitute the value calculated earlier for the fill rate (in cm^3/s):
dh/dt = (12 liters/min) * (1000 cm^3 / 1 liter) * (1 min / 60 s) / 50

After performing the calculation, we find the rate at which the height of the water in the tank increases, expressed in millimeters per second.

one liter is 1000 cm^3

Since the base has an area of 50cm^2, it takes 50cm^3 to cover it to a depth of 1 cm.

So, at 12000cm^3/min, the water level is rising at

(12000cm^3/min)/50cm^2 = 240cm/min