Water is withdrawn from a conical reservoir, 8 feet in diameter and 10 feet deep (vertex down) at the constant rate of 5 ft³/min. how fast is the water level falling when the depth of the water in the reservoir is 5 ft? ().

Water level in the reservoir is falling at the rate of 0.398 ft per minute.

Step-by-step explanation:

From the figure attached,

Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.

Let the level of water in the reservoir after time t is h where radius of the water level becomes r.

ΔABE and ΔCDE are similar.

Therefore, their corresponding sides will be in the same ratio.

--------(1)

Now volume of the water V =

From equation (1),

V =

V =

Since feet³ per minute and h = 5 feet

feet per minute

Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.

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step-by-step explanation:

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step-by-step explanation: