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 September 21st, 2015, 09:42 AM #1 Newbie   Joined: Sep 2015 From: mexico Posts: 10 Thanks: 0 water leaks out of cone Water leaks from the bottom of a cone at a rate of 1ft^3/min. (radius is 6 and height is 9) A) at what rate is the level of the water changing when the water level is 6ft deep? This is -1/4pi ft/min B) at what rate is the radius of the water changing when the water is 6 ft deep? This is -1/12pi so this is where I'm stuck (left a & b maybe could be helpful idk). Assume that at time 0 the tank is full. At what rate is the radius of the water changing at t=6? Last edited by skipjack; September 21st, 2015 at 06:27 PM. September 21st, 2015, 11:16 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1588 $\dfrac{r}{h}=\dfrac{6}{9} \implies h=\dfrac{3r}{2}$ $V=\dfrac{\pi}{3}r^2 \cdot \dfrac{3r}{2}=\dfrac{\pi}{2}r^3$ $\dfrac{dV}{dt}=\dfrac{3\pi}{2}r^2 \cdot \dfrac{dr}{dt}$ substitute 1 for $\dfrac{dV}{dt}$ and separate variables ... $\dfrac{2}{3\pi} \, dt = r^2 \, dr$ integrate ... $\dfrac{2t}{3\pi} + C = \dfrac{r^3}{3}$ when $t=0$, $r=6$ ... $C=72$ solve for $r$ in terms of $t$ ... $r=\sqrt{\dfrac{2t}{\pi}+216}$ from this point, you should be able to determine $\dfrac{dr}{dt}$ when $t=6$ Tags cone, leaks, water Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ganesh Ujwal Physics 2 January 3rd, 2015 06:47 AM leo255 Calculus 1 October 22nd, 2014 01:40 PM urduworld Calculus 2 November 1st, 2009 03:06 AM urduworld Calculus 2 October 31st, 2009 05:31 AM Silvester Algebra 0 February 17th, 2009 09:29 AM

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