A tank of water has a base a circle of radius 2 meters and vertical sides. If water leaves the tank at a rate of 4 liters per minute, how fast is the water level falling in centimeters per hour? [1 liter is 1000 cubic centimeters]

In 1 minute, 4 litre water leaves = 4*1000 cubic cm = 4000 [tex]* (10^{-2} )^{3} m^{3}= 4000 * 10^{-6 } m^{3} = 4 *10^{-3 }m^{3} [/tex]
so, the height decrease = Volume/area =
[tex] \frac{4*10^{-3}}{ \pi *2^{2}} \\ = \frac{4*10^{-3}}{4*\pi} \\ = 10^{-3}/\pi = 0.318 * 10^{-3} m = 0.318 cm[/tex]

hence water level in cm falling per min = 0.318
hence water level in cm falling per hr= 0.318 * 60 = 19.09

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facundo3141592 facundo3141592 · Answer 2 · 2022-01-27T11:46:37+01:00

We will see that the water level decreases at a rate of 1.91 centimeters per hour.

How to find the rate of change?

If we know the volume V of water in the cylinder, we can get the height at which the water is.

Remember that the volume of a cylinder of radius R and height H is given by:

V = pi*R^2*H

Then we have:

H = V/(pi*R^2)

meaning that if the volume decreases, also does the height (or level) of the water, as expected.

Now we know that the water volume decreases at a rate of 4 liters per minute, so we have a change in volume:

V = - 4 L/min

We want to write this in cm^3/h

1 L = 1,000cm^3

-4 L/min = -4,000 cm^3/min

1 hour has 60 minutes, so in one hour the volume lost is 60 times the volume lost in one minute, then the rate becomes:

60*(-4,000) cm^3/h

-240,000 cm^3/h

To get the change in level, we replace this in the equation for the water's height, where:

pi = 3.14
R = 2m = 200cm

H = (-240,000 cm^3/h)/(3.14*(200cm)^2) = -1.91 cm/h

So the water level decreases by 1.91 centimeters each hour.

If you want to learn more about rates of change, you can read:

https://brainly.com/question/8728504