related rates cone problem. water is leaking out at the same time as being filled

1 ANSWERS

1. amomipais82
   

   Hi,
   Variables -
   V= volume of cone
   r= radius of cone
   h= height of cone
   
   Rates:
   dh/dt = 6 in/min
   dr/dt = (is this also 6 in/min since the radius is always the same as the height?)  <<  YOU GOT IT.  BUT YOU COULD JUST WRITE  r = h
   dV/dt = unknown
   
   V= (1/3)pi*r^2*h  << AND MAKE THIS  (1/3) pi r^3,
   which would simplify things.
   
   r=h, so V= (1/3)pi*(h^2)*h = (1/3)pi*(h^3)
   
   >> AHA! I spoke too soon.  YOU did get it.
   
   dV/dt = pi(h^2)(dh/dt)
   h=10, dh/dt= 6
   
   dV/dt = pi(100)(6)
       = 600 pi or 1884.954 in/min

   Report (0) (0)  |   12 years, 7 month(s) ago