Sand is being poured at the rate of 0.3m3/s into a conical pile. If the height of the conical pile is thrice the radius of the base, find the rate of change of height when the pile is 5m high.

Dear Student ,
Please find below the solution to the asked query :

Let h be the height , r be the radius and v be the volume of cone.h=3rr=h3So,v=13πr2h=13πh32h=127πh3dvdt=327πh2 dhdt0.3=327πh2 dhdtdhdt=0.3×9πh2dhdth=5=0.3×9π52=2.725π=27250π cm/s .
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