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Question

A cylindrical tank with radius 5 m and height 5 m is full of water. The water is being drained at the rate of 4 m3/minute.

How fast is the water level dropping when the water level in the tank is at half its height? Give your answer as an exact expression.

 

The answer is 4/25π but I don't know understand why.

 

thank you for the help

Answer 1

The bit about "when the water level in the tank is at half its height" is not needed.  The rate of the level dropping is how far the level drops per minute.  The volume of water drained per minute is 4 m³. That amount of water represents the area of the cylinder's base (πr²) times some height (h). That height is the level drop per minute.

Radius r=5

πr²h = 4

n(5²)h = 4

25nh = 4

h = 4 / (25n)

Hope this helps