A pool in the shape of a cylinder with a height of 6 m and a base radius of 7 m is drained for repair. If the rate at which the pool is being drained is 3 m3/min, find the rate at which the water level is falling when the water is 4 m deep to the nearest hundredth.

The rate at which the water level is falling when the water is 4 meters deep to the nearest hundredth is 0.02 meters per minute.

Step-by-step explanation:

The volume of a cylinder (), measured in cubic meters, is represented by the following formula:

(1)

Where:

- Radius, measured in meters.

- Height, measured in meters.

Then, we differentiate (1) in time:

(2)

Where:

- Rate of change of the volume, measured in cubic meters per minute.

- Rate of change of the radius, measured in meters per minute.

- Rate of change of the height, measured in meters per minute.

Then, we clear the rate of change of the height:

(3)

If we know that , , and , then the rate of change of the height is:

The rate at which the water level is falling when the water is 4 meters deep to the nearest hundredth is 0.02 meters per minute.

step-by-step explanation:

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