Question
Wed January 09, 2013 By: Rajeshmudgal
 

water is dripping out from a conical funnel at a uniform rate of 4cm cubic/sec through a tiny hole at the vertex in the bottom.when the slant height of the water is 3cm ,find the rate of the decrease of the slant height of the water,given that the vertical angle of the funnel is 120

Expert Reply
Thu January 10, 2013
rate of dripping of water from conical funnel=dv/dt=4c.m cubic/sec
                                                             volume of water v=1/3pi r^2h
                                         also sin60=r/l
                                                  r=(root3)/2*l
                                                 cos60=h/l
                                                  h=l/2
using in volume
                          v=(1/3)*pi*3/4*l^2*l/2
                            =(1/8)*pi*l^3
   diff. w. r. to t
                         dv/dt=(1/8)*pi*3(l^2)(dl/dt)
                          atl=3, dv/dt=4
      so dl/dt=(4*8)/27pi
                = 32/(27pi) c.m./sec  
 
 
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