The water level raising at the instant the cone is completely submerged.
A cone of radius and height is lowered point first at a rate of in a tall cylinder of radius cm which is partially filled with water.
Let be the depth that the cone is submerged.
We are given that
The volume of water that is displaced is given by the formula ,
where is obtained from the relation
Now differentiating the volume we get,
When the cone is completely submerged, and we have .
Let denote the water level in the cylinder.
Then the volume of water in the cylinder is given by ,
and we have .
Putting in the value of , and solving for , we get,
Thus we can say that the water level is rising at a rate of cm/s at the instant the cone is completely submerged.
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