Andrew F. answered • 11/11/21
Experienced private school teacher
Hello Jenna. The key to this is to translate English words into Calculus symbols and understand what is going on. Volume for water inside a cylinder is "V" and the instant rate of change for the volume (total amount) of water is "dV/dt" (how the amount of water is changing as time moves on). The height of the water is "h" and remember what many students don't see with this problem: the radius of a cylinder is constant, so the derivative is easy to find. V = (pi)(6^2)(h) so the derivative is dV/dt = (pi)(6^2)(dh/dt) then plug in the negative 3 for dV/dt and you have the answer. Does it make sense visually that dh/dt is always the same for a cylinder?
Andrew F.
Jenna, you are correct that we don't use/need those numbers, but it's really important to understand why. Soon--maybe even on the same assignment as this one--you will be asked a similar question with a cone instead of a cylinder. Picture water draining out of a cylinder and you see the same circle of water on the top the entire time--this is why the change in height is a constant no matter how much water is in this 6ft radius cylinder if the amount of water leaving is constant. If you picture water draining out of a cone, then you see a circle on top which gets smaller and smaller--if the amount of water leaving a cone is constant and the circle of water you see on top is getting smaller, then the change in height of the water is not constant (see if you understand this--does the height change faster or more slowly as water drains out of a cone?) Hope this makes sense.11/12/21
Jenna T.
so do we not use the 20 or the 15?11/11/21