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 February 10th, 2013, 01:35 AM #1 Newbie   Joined: Jan 2013 Posts: 3 Thanks: 0 Help me with this question pretty please Diagram shows a conical container of diameter 0.8m and height 0.4m. Water is poured into the container at a constant rate of p m^3 s^-1. Calculate the value of p, given that the rate of change of the height of the water level is 0.1ms^-1 at the instant when the height of the water level is 0.2m. (Use ? = 3.142 and volume of cone = 1/3?r^2h) Show me the working please. Thanks a million!
 February 10th, 2013, 05:09 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Help me with this question pretty please Are you taking a Calculus course? This is a pretty standard Calculus question and examples are given in any Calculus text. You really need to at least try to do this yourself. You have stated the formula for volume, $V= (1/3)\pi r^2h$. That's good! Knowing that the container has "diameter 0.8m and height 0.4m" (so radius .4 m) can you see that the water in it, at any height will form a cone with equal radius and height, r= h? Replacing r with h will give a formula for V in terms of h only. Differentiating both sides with respect to t will give a formula relating the rate of change of V to the rate of change of h.

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