Thread: Volume 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?

Originally Posted by symmetry

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?

a)

Thus:






b) If then






-Dan

Dan,

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

I did not follow that part.

Thanks!

Originally Posted by symmetry

Dan,

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

I did not follow that part.

Thanks!

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

I finally got it.

Thanks!