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calculus

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Is it possible to find an example of a bounded region in the x, y plane that satisfies the following condition : when you revolve the region about the x axis you obtain a solid that has a volume equals its surface area

  • calculus -

    yes :)
    do you want me to cite an example?

  • calculus -

    please i need an example !

  • calculus -

    please can you give me an example?

  • calculus -

    please can you give me an example?

  • calculus -

    sorry i haven't replied to your reply earlier. anyway, here's an example:

    there are many possible examples for this. but since we need to calculate volume (V) and surface area (SA), we choose a figure where its V and SA can easily/readily be calculated.
    for instance we want to generate a shape of a cylinder,, note that this only requires a line parallel to x-axis (but not passing through x-axis) so that if it's revolved about the x-axis, it becomes a cylinder, or y = c, where c = any real number except zero. now we only need to find the bounds. for simplicity, let's choose one of the bounds as the origin.
    recall that the V and SA of a cylinder is given by
    V = π(r^2)*h
    SA = 2πrh + 2πr^2
    where r is radius and h = height
    then we choose a value for V and SA . let's choose, for instance, 100 :
    V = 100 = π(r^2)*h
    SA = 100 = 2πrh + 2πr^2
    since there are two equations, two unknowns, by substitution, we get two pairs of answers:
    (i) r = 2.218 ; h = 20.327
    (ii) r = 5.696 ; h = 3.08219
    here, let's just choose (i).
    when the equation y = c is revolved, the cylinder generated has a symmetry on x-axis (like it's lying/rolling on the floor). thus the radius is the y-coordinate and height is the x-coordinate. therefore y = c becomes
    y = r = 2.218
    with bounds from origin (0,0) to its height (20.327, 0)

    hope this helps~ :)

  • calculus -

    thank you alot for your help I was really worried because i have to submit the answer tomorrow and i could not do any thing without your help
    thank you again

  • calculus -

    you're welcome~ :)
    by the way, i just want to make a correction. fro the value of V and SA, it's not 100, it should be 100*pi = 314.16 . sorry i forgot the pi, because i cancelled it right away, but the answers for r and h is still the same. i'll just retype the correction:
    ...then we choose a value for V and SA . let's choose, for instance, 100*pi :
    V = 100*pi = π(r^2)*h
    SA = 100*pi = 2πrh + 2πr^2
    ...and the rest are correct.

    so, the value of V and SA for the dimensions (i) and (ii) we got is equal to 100*pi or 314.16, not 100. sorry~ :P

  • calculus -

    thenk you jai and sara
    in which section you are sara?

  • calculus -

    sectin 20 what about you?

  • calculus -

    section 70
    nice to meet you
    if you need any help just tell me
    from wich college you are?

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