<p>Hey can somebody please help me with this question? thanks so much in advance! :)</p>
<p>Water is draining from a conical tank with height 12 feet and diameter 8 feet into a cylindrical tank that has a base with area 400pi square feet. The depth, h, in feet, of the water in the conical tank is changing at the rate of (h-12) feet per minute.</p>
<ol>
<li><p>Write an expression for the volume of water in the conical tanks as a function of h.</p></li>
<li><p>At what rate is the volume of water in the conical tank changing when h=3? (include units of measure)</p></li>
<li><p>Let y be the depth, in feet, of the water in the cylindrical tank. At what rate is y changing when h=3? (include units of measure)</p></li>
</ol>
<p>1) Use your algebra. This should be self-explanatory.</p>
<p>2) Use the Product Rule to get dV/dt. See what variables are missing. According to my calculations, it looks like you’re missing the variables r and dr/dt. (Note: Since this is a cone, the radius does change as volume change; at any given value for height, there is a different value for radius) Solve for those variables (hint: use proportions to find radius at h = 3. Also, you may have to use 2 dV/dt equations because you need to solve for dr/dt afterwards) Then put everything together, solve for the final dV/dt value. dV/dt should come out as a negative value.</p>
<p>3) Volume of cylinder = pi x r^2 x y (y = h, where h is height). Using the area equation given for the base of the cylinder, find the radius (r comes out to be 20). To find the answer to that question, do the same thing you did with part 2, except this time you’re using a volume formula for a cylinder. (Hint: You may have to use dV/dt that you found from part 2, but this time, since the cylinder is increasing in volume, the dV/dt should be positive)</p>
<p>sorry but I think i figured it out! just wanted to say before you spend time on it. but i didn’t get something else.</p>
<p>The length of a solid cylindrical cord of elastic material is 32 inches. A circular cross section of the cord has radius 0.5 inch. </p>
<p>The cord is stretched lengthwise at a constant rate of 18 inches per minute. Assuming that the cord maintains a cylindrical shape and a constant volume, at what rate is the radius of the cord changing one minute after the stretching begins? (include units of measure)</p>
<p>thanks so much!</p>