[meteor_slideshow slideshow=”arp1″]
You are asked to make a filtering device to purify the drinking water. This device consists of two parts: a cone-shaped container placed upside down, with a small hole at the tip of the cone. Partly because of the pressure due to gravity, water is leaking at a rate which is proportional to a certain funtion of the weight. 1. You are asked to make the cone-shaped container with the largest volume from a circular piece of sheet metal with a radius √3 meters. How can you do that? Assume that the water is leaking out from the cone-shaped container at a rate which is proportional to the square root of the weight. Since the weight is directly poroportional to the volume, water is leaking at a rate which is described by = k√V m3/minute, here k = -2. 2. At the moment when exactly half of the water has leaked out of the container, how fast is the water level in the cone falling? 3. You are asked to make the bucket with a total volume of π m3 by using the least amount of material. How can you do that? 4. At the moment when exactly half o fthe water has leaked out of the container, how fast is the water level in the bucket rising? 5. How long will it take for the cone to get empty? 6. How would you improve this model?
[meteor_slideshow slideshow=”arp2″]
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