Deriving The Formula - Volume Of Sphere
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Awesome man! exactly what i was searching for!!
i'm making this for my maths model..
only if i'd find these cylinder and sphere... i'd get A+ for sure..!
zeke2812 3 months ago
You can't Derive mathematical truths by experiment. You must use proof. Sigh.
mattymath1 4 months ago
very nice demonstration of the fact that the volume of a sphere is two thirds the volume of the cylinder with the same radius and a height equal to the diameter. not a derivation of the formula by mathematical standards, but perhaps by experiment.
DarthPickley 7 months ago 2
What no formula come on!!!
p0larz0mbies 8 months ago
That isn't a proof at all, to do this you need calculus, use integration, volumes of revolution to be more exact. Take the curve, y^2 + x^2 = r^2 rotate around either the x or y axis, using integration find the volume, and multiply your final result by 2...
Yu2Kal 1 year ago
(continued) Also, the volume of a cylinder is basically equal to the area of a circle at the base of the cylinder = (PI) r^2 , and then multiply this area by the height of all the unit volumes (ie where h=1) for each and every cylinder segments:
Volume of cylinder = (PI) r^2 h
trailkeeper 1 year ago
Very clever and entertaining, but I'm sure you are aware it's knowledge by induction.
ski2golf 1 year ago
@partonfilaton you only need a single integration ;).
elfmotat 1 year ago
how is that deriving the formula??
im too confused i didnt get the double integration part... but that's probably because IT WASNT THERE
partonfilaton 1 year ago
You can also derive the formula for the volume of a sphere of radius a using cylindrical coordinates by taking the triple integral of r and having the bounds of z, r, and theta be 0 to Sqrt(a^2-r^2), 0 to a, and 0 to 2Pi, and then multiple the final answer by 2.
tyler121515 2 years ago