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Volume of a Described Solid

  1. Jan 23, 2012 #1
    1. The problem statement, all variables and given/known data
    I uploaded of a picture of the question so hopefully it comes up here.

    2. Relevant equations

    3. The attempt at a solution

    OK! so i am SO confused on where to start.
    I am imagining the solid flipped on its side with the x axis going through its center.

    So all i have is that the integral would be from 0 to h of (pi)(r)^2
    Is this at all close?
    Any hints would be greatly appreciated. :)

    Attached Files:

  2. jcsd
  3. Jan 23, 2012 #2


    Staff: Mentor

    That's a start but you have to relate r to h and then integrate over h.
  4. Jan 23, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper

    r, R and h are given as constants in your diagram. Let's not integrate over any of them. Let y be the distance from the bottom of your solid. So y goes from 0 to h. Then your integral is the integral of (pi)(ρ(y))^2*dy for y from 0 to h. Where ρ(y) is the cross sectional radius of your solid at the height y. ρ(0)=R, ρ(h)=r. Can you figure out an expression for ρ(y) at a general height y?
  5. Jan 24, 2012 #4
    I GOT IT !
    thanks for the help dick :)
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