Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    c. x=s
    d. i don't know
    e. i don't know
    f. [0,2pi]

    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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor

    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??
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook