# SpheresWatch

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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?
0
14 years ago
#2
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.
0
14 years ago
#3
Yeah, it is.
V = INT[0,r] of area function
So surface area = lim(x->r) of area function.
I think
0
14 years ago
#4
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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#5
(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.

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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14 years ago
#6
(Original post by Princess Ana)

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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#7
Never mind. I'm confused. Just walk away slowly...
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