The inside of a funnel of height aa inches has circular cross-sections as shown in the image above. At height h, the radius of the funnel is given by \(r={{qq + h^2} \over cc}\) where \(0 \le h \le a \)
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(a) Find the average value of the radius of the funnel s
The answer is \({{qq \over {cc}} + {aa^2 \over {3*cc}}} = {finalAnswer}\) inches
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(b) Find the volume of the funnel
The answer is \({\pi \over cc^2} * (aa \times qq + {aa^5 \over 5} + {aa^3 \over 3}) = {finalAnswer}\) inches \(^3\)
The funnel contains a liquid that is draining from the bottom. at the instant when the liquid is \(h = d_d \) inches, the radius of the surface of the liquid is decreasing at a rate of \(1 \over ee \) inch per second.
(c) At this instant, what is the rate of change of the height of the liquid with respect to time?
The answer is \({-cc \over {2 (ee \times d_d)}} = {simplifiedAnswer} = {finalAnswer}\) inches per second
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(d) ___
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