Calculus Help!!

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1

<p>Hey everyone I was just wondering if any really smart person could help me with some Calculus problems. I try so hard but I just cannot understand how to do these....I seriously hate this class :( Anyways, if anyone can help, thanks alot!</p>

<p>1) At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 15 feet high?</p>

<p>2) A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.</p>

2

<p>1)The height is 15 feet, therefore the diameter of the base must be 45 feet.</p>

<p>V = 1/3 pi r^2 h
dV = 1/3 pi r^2 dh + 2/3 pi r h dr
3 * 2r = h ---> 6 dr = dh
dV = 1/3 pi r^2 dh + 2/3 pi r h (dh/6)</p>

<p>dV = 10
r = 45 / 2
h = 15
solve for dh :-)</p>

3

<p>is the answer 0.859 ft per minute?</p>

<p>If it is correct, I will post the solution.</p>