Question 713125: An inverted conical tank of radius 3 meters and altitude of 9 meters contains water to a depth of 3 meters. How much water must be added into the tank such that the depth of water will be doubled?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The tank volume is radius squared times pi, times height, divided by 3.
In cubic meters, that is 3 squared, times pi, times 9, divided by 3,
which calculates to 27pi
The water in the tank occupies a similar cone,
with all dimensions proportionally smaller by a factor of 3.
That volume is smaller by a factor of 3 cubed, or 27.
So the volume of water in the tank is pi cubic meters.
The volume when the water is twice as deep is the volume of a similar cone,
2 times as large in all dimensions.
That makes the volume larger by a factor of 2 cubed, or 8.
The amount of water that needs to be added is 7 times what is in the tank,
or 7pi cubic meters.
That is about 22 cubic meters, which is 22,000 liters.
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