Finding the Relationship Between Volume and Surface Area of a Sphere

[david18]

The Volume and surface area of a sphere is 4/3πr^3 and 4πr^2 respectively. V=4/3πr^3 and S=4πr^2. Write a) S in terms of V and b) V in terms of S

Im stuck on this question... I write out similar base units and stuff but it doesn't seem to work, any help?

-The answer to part a is S=2^2/3 3^2/3 π^1/3 V^2/3

 

[Diffy]

Apparently what you have to is solve each formula for r, and then plug into the the other.

So to solve part a) first, solve your Volume formula for r. then plug that into r in your S formula.

Just do the opposite to solve part b.

 

[symbolipoint]

The Volume and surface area of a sphere is 4/3πr^3 and 4πr^2 respectively. V=4/3πr^3 and S=4πr^2. Write a) S in terms of V and b) V in terms of S

Im stuck on this question... I write out similar base units and stuff but it doesn't seem to work, any help?

-The answer to part a is S=2^2/3 3^2/3 π^1/3 V^2/3

At least use grouping symbols properly if you do not have mathematical typesetting formatting. You intend to say
[tex] \[
V = \left( {\frac{4}{3}} \right)\pi r^3 \quad S = 4\pi r^2
\]
[/tex]

You should see through inspection that S is actually contained in the formula for V.
[tex] \[
V = \left( {\frac{1}{3}} \right)(4\pi r^2 )r = \frac{{Sr}}{3}
\]
[/tex]
Right now, I do not yet see a way to completely eliminate 'r' from the formula. ...Should be possible though.

 

[symbolipoint]

David18 has the right method. It will look a little messy but it will work. No need to bluntly show variable r.