I was just looking over my notes and I do not understand this question entirely
A cone with height 10ft and top radius 5ft is filled with oil which weighs 57lb/ft^3. find work done in pumping out the oil.
I know that the interval being sliced is [0,10] because the oil fills the entire tank.
I also understand why the the distance is (10-y)
What I do not understand according to my notes is where (y^2) comes from. Or where the radius comes into play?
If it is coming from the formula for a cone 1/3pi*r^2 then why does my notes say the final answer is
I thought it should be
If you look at the diagram you will see why. We have the roles of y and y-10 exchanged in our diagrams. This is unimportant the integrals are equivelent. Basically I didn't notice that you have your coordinate system starting at the bottom of the cone where mine is at the top.
if you let
Remember the way you set up alot of these is not unique.
Sorry my wife found it for me and it is supposed to be Raistlin Mejere from Dragon lance. I can ask her where she got it when she gets home from school. off topic I just played my first oblivion game on PS3 and it was awsome. On topic
We are using the height as dy so on the small scale each slice is approximated by a cylindar. Think of it as we are cutting little circular disks of height dy