## Area of a sphere

How do you find the area of a sphere based on it's volume?

 Recognitions: Gold Member surface area of sphere: 4pi r^2
 Well, usually you find both of the above based on the circle. Integrating half a circle's arc length gives surface area, and integrating half a circle's area gives volume. However, the sphere's volume [itex] \frac{4}{3}\pi r^3 [/tex], and surface area [itex] 4\pi r^2 [/tex] are related as integrals/derivatives of the radius 'r'.

## Area of a sphere

Can you put that in an equation form like Area= volume x _ ?

 Recognitions: Gold Member You mean turn the volume into the SA?

 Quote by yomamma You mean turn the volume into the SA?
Yes .

 Well I guess a really ugly way of doing it is just saying $$SA = \frac{3V}{r}$$ Do you know calculus?
 No, i just finished algebra II. Is there another way to say it? Without having to first calculate radius?
 Recognitions: Gold Member Science Advisor Staff Emeritus You have all you need to figure that out yourself...
 Recognitions: Gold Member Homework Help Science Advisor Serj: Do you agree that the radius r in terms of volum V is: $$r=(\frac{3V}{4\pi})^{\frac{1}{3}}$$?? Use this to express the surface area in terms of the volume.
 Blog Entries: 9 Recognitions: Homework Help Science Advisor Serj,the sphere's volume ("it's (sic!) volume") is zero...So the area is simply $$\mbox{Area}_{\mbox{Sphere}} =\mbox{Area}_{\mbox{Sphere}} \ + 0$$ $$\Longrightarrow \mbox{Area}_{\mbox{Sphere}} =\mbox{Area}_{\mbox{Sphere}} \ + \ \mbox{Volume}_{\mbox{Sphere}}$$ Daniel. P.S.Apart from the notation,there's no joke in this post...
 Recognitions: Gold Member Homework Help Science Advisor Daniel is of course right. You are to express the sphere's area in terms of the enclosed ball's volume.
 Recognitions: Homework Help I could see that one coming a mile away. LOL !! :D
 Recognitions: Gold Member Science Advisor Staff Emeritus $$A = (36 \pi V^2)^{1/3}$$ - Warren
 Recognitions: Homework Help Science Advisor to find the volume of a sphere one computes how the volume form the portion of the sphere at or below height y, changes as y changes. it turns out that the rate of change of the volume at height y, equals the area of the circular slice at height y. from this one can write a formula for the dertivative of the rising voilume formula, and from that one can write a formula for the volume of a sphere of radius R as (4/3)pi R^3). then one writes the volume of the sphere in terms of the radius, and sees that the rate of change in that case, at the point where the radius is r, equals the area of the sphere of radius r. Since we know the volume, and that the area is the derivative of the volume wrt the radius, we get that the area is 4 pi R^2. so first you find the volume of the sphere, knowing the area of a circle. Then knowing the volume of a sphere you find the area of the sphere. I am not sure, since I have not seen his works, but i suspect this is the way Archimedes did it.

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Homework Help
 Quote by chroot $$A = (36 \pi V^2)^{1/3}$$ - Warren