  Help me with Calculus problem

<p>Well actually two.<br>

<p>1) Water is being poured into a conical reservoir at the rate of pi cubic feet per second. The reservoir has a radius of 6 feet across the top and a height of 12 feet. At what rate is the depth of the water increasing when the depth is 6 feet?</p>

<p>2) A man 6 feet tall is walking toward a lamppost 20 feet high at a rate of 5 feet per second. The light at the top of the lamppost (20 feet above the ground) is casting a shadow of the man. At what rate is the tip of his shadow moving and at what rate is the length of his shadow changing when he is 10 feet from the base of the lamppost?</p>

<p>I learned this today</p>

<p>1) Rewrite the volume equation for a cone (v=1/3(πr²h) in terms of h, since we're dealing with change in depth. We can do this by using similar triangles, since the ratio is r/h is proportional to 6/12, r=1/2h. Substitute that into the cone volume equation to get V=1/12(πh³). Now it's just a matter of taking the derivatives, substituting, and simplifying:</p>

<p>The derivative of (V=1/12(πh³) translates to dv/dt = 1/4(πh²) * dh/dt.
Substitute what you know: dv/dt=π , h=6 , dh/dt = unknown</p>

<p>π=1/4(π*6²) * dh/dt
dh/dt = 1/9, and in units, 1/9 ft/sec</p>

<p>Isn't this homework help? I thought it wasn't allowed on CC.</p>

<p>You must be pretty behind, our class learned that over a month ago.</p>

<p>No homework help here... We operate on a higher topos</p>

<p>Why is homework help prohibited here? And who is to say this is homework? What differentiates someone helping me with this math problem and someone helping someone else with an SAT or ACT question? That distinction is so arbitrary.</p>

<p>And BioGen---Thank you SO MUCH! I really truly appreciate it.
BiovBall-- It depends. There are multiple types of Calc classes-2 levels of AP Calc. AB and BC, Honors Calc, etc..</p>