A belt placed round a sphere has area 2πrh where r is the radius of the sphere and h is the width of the belt.
A cap on a sphere, i.e the intersection of a sphere with a cone with the point at the centre of the sphere, of height h, has to an area of 2πrh.
I'd like a method to show the equivalence of these two geometrical areas without resorting to deriving them both separately. Something which is more intuitive for those without a mathematical bent.
Anyone any ideas?
A cap on a sphere, i.e the intersection of a sphere with a cone with the point at the centre of the sphere, of height h, has to an area of 2πrh.
I'd like a method to show the equivalence of these two geometrical areas without resorting to deriving them both separately. Something which is more intuitive for those without a mathematical bent.
Anyone any ideas?
via International Skeptics Forum https://ift.tt/2I4i3Sz
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