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Ana
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#1
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#1
Is it a coincidence that the derivative of the formula for the volume of a sphere (V=4/3*pi*r^3) is the same as the formula for the surface area of said sphere, ie 4*pi*r^2, or is there a reason behind this?
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SsEe
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#2
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I'd say coincidence. Also, parametrically a parabola is given by (at², 2at). See the derivative? Another coincidence methinks. Though I'd very much like to know what somebody who's more experienced than me thinks.
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BCHL85
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Yeah, it is.
V = INT[0,r] of area function
So surface area = lim(x->r) of area function.
I think
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RichE
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No it's not a coincidence - and similarly 2 pi r and pi r^2 for circles - because one could calculate the area of the circle by integrating concentric circles within.

The parabola example seems to be coincidence - given you could change parameter (e.g. t = u^3) and get two functions that aren't derivatively-related. However it may be that t is a preferential parameter and so it not be coincidence - I haven't really put any thought into this.
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Ana
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(Original post by RichE)
No it's not a coincidence - and similarly 2 pi r and pi r^2 for circles - because one could calculate the area of the circle by integrating concentric circles within.
I've been thinking about this since, and something puzzles me...

Why is the formula for the surface area of a cube 6x^2 and not 3x^2 ? What makes the difference?
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RichE
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(Original post by Princess Ana)
I've been thinking about this since, and something puzzles me...

Why is the formula for the surface area of a cube 6x^2 and not 3x^2 ? What makes the difference?
If x is the length of an edge, then it's simply because a cube has six square faces each with area x^2.

Why should it be 3x^2?
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Ana
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#7
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Never mind. I'm confused. Just walk away slowly...
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