SOLUTION: Water is being pumped into a conical tank at the rate of 100 ft3/min. The height of the tank is 20 ft and its radius is 5ft. How fast is the water level rising when the water heig

Question 650834: Water is being pumped into a conical tank at the rate of 100 ft3/min. The height of the tank is 20 ft and its radius is 5ft. How fast is the water level rising when the water height is 10ft?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Water is being pumped into a conical tank at the rate of 100 ft3/min. The height of the tank is 20 ft and its radius is 5ft. How fast is the water level rising when the water height is 10ft?
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The volume of a cone,
We can express r in terms of h: r = h/4
So we have an equation for the volume in terms of the height only:

The rate of change of volume,

The rate of change of the water height, , at h=10 is:

So the rate of rise at h=10 ft = 5.093 ft/min
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