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

Asked by RajeshMudgal | 9th Jan, 2013, 07:08: PM

Expert Answer:

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  
 
 

Answered by  | 10th Jan, 2013, 02:59: PM

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