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Expert: - 2/29/2008


Question
Slag left over from the manufacture of cement is being piled outside a cement plant. The resulting slag heap is a cone. The side of the cone make an angle of 40degrees with the horizontal. Environmentalists measure the circumference of the heap one day, finding it to be 3000ft, and increasing at 10 ft/day. About how fast is the cement plant generating slag?

Answer
The equation for the volume of a cone is (pi)r^2h/3 where r = radius of the base, h=height in the middle.  The perimiter of the base is
2(pi)r.  dV/dt = 10ft/day. Circumference = 3000.  The height h over the circumference c, h/c, is the tan(40).  Use these to find the rate of change of volumne (since that's the amount of slag) with respect to the change in the circumference of the cone.

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