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Thread: Surface Area of a circular strip from a sphere

  1. #1
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    Surface Area of a circular strip from a sphere

    Some one help me, please. I do not understand the problem.

    Show that for any numbers r, a, and h so that r, h > 0 and  -r\leq a< a+h\leq r that the circular strip formed by truncating a sphere of radius r between x = a and x = a+h has the same surface area regardless of a. I.e, show that this value is not dependent on a.

    In my opinion, the area of the circular strip is largest when it is on the middle of the sphere and it is smallest at top. But it sounds wrong when the question is about proving they are all equal.
    Last edited by Loser66; Aug 10th 2017 at 05:06 PM.
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  2. #2
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    Re: Surface Area of a circular strip from a sphere

    $\displaystyle S = 2\pi \int_a^{a+h} y \cdot \sqrt{1 + \left(\dfrac{dy}{dx}\right)^2} \, dx$

    where $y=\sqrt{r^2-x^2}$

    Evaluate the surface area integral for $S$ ... you'll find that its value is independent of the value of $a$.
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  3. #3
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    Re: Surface Area of a circular strip from a sphere

    Thank you so much. I thought too much.
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