Question #248975

A cone of radius 2 cm and height 5 cm is lowered point first into a tall cylinder of radius 7 cm that is partially filled with water. Determine

how fast the depth of the water is changing at the moment when the cone is completely submerged if the cone is moving with a speed of

3 cm/s at that moment.




1
Expert's answer
2021-10-10T09:34:08-0400


adding πr2on\pi r^2 on Both sides


π22=π72×dX/dtπ 2 ^2 = π 7 ^2 \times d X/ d t


divide both side by :π72\pi 7^2


22/72=dX/dt2^ 2 /7 ^2 = d X /d t




thus change in water level with time is 449cmsec\frac{4}{49}\frac{cm}{sec}

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