calculus

posted by .

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?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
  2. calculus

    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
  3. Calculus

    a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 …
  4. Calculus

    Let R be the region bounded by the x-axis, x = 5 and the curve y = x. This region is rotated around the x-axis. Find the volume of the resulting solid. (Note: R is a triangular region. The resulting solid has a simple shape. You may …
  5. CALCULUS MAJOR HELP!!!!!!

    Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume …
  6. Calculus volume stuff

    Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume …
  7. Calculus I don't understand

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x …
  8. CALCULUS HELP PLZ

    The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is divided …
  9. CALCULUS

    The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is divided …
  10. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the …

More Similar Questions