# Homework Help: Relating Surface area to volume

1. Aug 30, 2010

### juice34

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

2. Aug 30, 2010

### Staff: Mentor

(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?

3. Aug 30, 2010

### juice34

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

4. Aug 30, 2010

### Staff: Mentor

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

5. Aug 30, 2010

### 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

6. Aug 30, 2010

### Staff: Mentor

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?

7. Aug 30, 2010

### 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.

8. Aug 30, 2010

### juice34

Here lets 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?

9. Aug 30, 2010

### Mentallic

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

10. Aug 30, 2010

### juice34

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