Send drops from A pipe at the rate 3 cubic feet/minute and forms a heap of cone on the ground of Vertical angle 90°. At what rate the height is increasing after 4 minutes.

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Solution

Given dv/dt=3
ass the expert explained above the radius is equal to the height..(refer the above figure)

So V=1/3πr²h
But r=h
So V=1/3πh³

The volume of the sand is 12
So considering it we will get height=(36/π)⅓

So now differenriating with respect to time
dv/dt=3=(1/3)π3h²dh/dt

So calculating it gives the result
(1/48π)⅓

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