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:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,