Relating Surface area to volume

[juice34]

How do I express the surface area of for instance a sphere in terms of volume?

 

[berkeman]

How do I express the surface area of for instance a sphere in terms of volume?

(question moved to homework help)

What is the context of your question. The surface area and volume of a sphere are straightforward formulas in terms of the radius. I'm guessing that there is more to your question?

 

[juice34]

I want to express the surface area of a sphere in terms of the volume and not radius.

 

[berkeman]

I want to express the surface area of a sphere in terms of the volume and not radius.

What are the two formulas for volume and surface area? What would be some way to do what you are asking?

 

[juice34]

V(sphere)=(4/3)*pi*R^3
S.A.(sphere)=4*pi*R^3

I am thinking i need to take derivatives, but when you do dV/dR you just get the surface area

 

[berkeman]

V(sphere)=(4/3)*pi*R^3
S.A.(sphere)=4*pi*R^3

I am thinking i need to take derivatives, but when you do dV/dR you just get the surface area

You meant R^2 in the area forumula.

I would think one way would be to express R as a function of volume, and then substitute that back into the area forumula for R... (or the other way around, depending on what you are wanting to do. Does that work?

 

[Mentallic]

Surface area is equal to $4\pi r^2$ and there are no need for derivatives, you have two equations, both with r in them so you want to eliminate r by substitution.

 

[juice34]

Here let's make this more complicated.
#1) V(sphere)=(4/3)*pi*(D/2)^3
#2)S.A.(sphere)=4*pi*(D/2)^3

So i solve to D using equation 1. D=(V(24/(4*pi)))^(1/3)
So can i just plug this D into #2 and wah lah?

 

[Mentallic]

Here let's make this more complicated.

Uhh yep, that's all there is to it... By the way, simplify 24/4pi, unless you like to keep things more complicated

 

[juice34]

Sometimes things look more complicated than they are, haha! THANKS GUYS