The volume of a sphere of radius r is V = (4/3)(pi)(r^3); the surface area S of this sphere is S = 4(pi)(r^2).

(a) Express the volume V as a function of the surface area S.

(b) If the surface area doubles, how does the volume change?

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- January 22nd 2007, 01:52 PMsymmetryVolume of Spheres
The volume of a sphere of radius r is V = (4/3)(pi)(r^3); the surface area S of this sphere is S = 4(pi)(r^2).

(a) Express the volume V as a function of the surface area S.

(b) If the surface area doubles, how does the volume change? - January 22nd 2007, 02:39 PMtopsquark
- January 22nd 2007, 03:38 PMsymmetryok
Dan,

Hello. How did you get r to equal (s/4pi)^(1/2)?

I did not follow that part.

Thanks! - January 23rd 2007, 05:55 AMtopsquark

Now, we need to take the square root of both sides. It was more convenient for me to express this as

rather than

Both of these forms are completely equivalent, though you would probably recognize the second as being more familiar. Perhaps I should have mentioned this when I solved the problem.

-Dan - January 23rd 2007, 05:23 PMsymmetryok
I finally got it.

Thanks!