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Finding an expression

  1. May 26, 2006 #1
    1.A cone where h= height of the cone
    s= slant of the cone
    r= radius of the cone



    a.Find c,circumference of a cone in terms of x
    b.find r, radius of the cone in terms of x
    c. find an expression for the slant height of the cone in terms of x
    d. find h, hieght of the cone in terms of x
    e. find the volume of the curve in terms of x in the form of
    V= (a-x)^2[(bx-x^2)^(1/2)]
    -----------------------
    c where a,b,c are positive
    f find the domain of the function
    g. find v'(x)

    what i have done:
    a. x=2pir
    b. r=x
    ---
    2pi
    c. x=s
    d. i don't know
    e. i don't know
    f. [0,2pi]
    g.????

    could someone please help me
    thank you
     
  2. jcsd
  3. May 27, 2006 #2
    its easy actually....draw a cone ....and then draw an imaginary circle along the contour of the cone ...and label its radius as r , and let it be at height of x from below... ...therefore height of the cone above this cricle will be [h-x] , so u get a smaller cone (upper one)... use pythagorus theorem , u can get the slant height of upper smaller cone using property of similar triangles...
     
  4. May 27, 2006 #3

    HallsofIvy

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    Frankly, the problem doesn't make a whole lot of sense. You are given h and r but then asked to write things "in terms of x"?? What is x? You appear to be assuming that x is r, even when the problem says "find r in terms of x", but that is not given in your problem.

    Assuming that x really is just r, then as Dr. Brain says- draw a picture. Looking at the cone from the side, it is an isosceles triangle height h and base 2r so each half is a right triangle with height h and base r. The slant height is the length of the hypotenuse so you can use the Pythagorean theorem.

    But then I run into "d. find h, hieght of the cone in terms of x".
    You are given two independent values, h and r. If x really is r, then there is no way to right h "as a function of x". Knowing r tells you nothing about h.

    "e. find the volume of the curve in terms of x in the form of
    V= (a-x)^2[(bx-x^2)^(1/2)]"

    The volume of the curve? Do you mean volume of the cone? The volume of a cone depends on both the height, h, and the radius, r, and they are independent. The volume cannot be written as a function of a single variable unless there is some relation between r and h you haven't given here.
     
  5. May 27, 2006 #4
    oops i meant cone
     
  6. May 28, 2006 #5

    HallsofIvy

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    Did you understand anything I wrote? The problem, as you stated it, still doesn't make sense. If you were really told to express these things "in terms of x", what in the world is x??
     
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