SOLUTION: I am trying to solve a problem relating the volume to the surface area of a sphere. I got this far and cannot finish it. Can you please help me? Thank you. v=4/3pi*(s/4pi)**3/2

Click here to see ALL problems on Radicals

Question 18435: I am trying to solve a problem relating the volume to the surface area of a sphere. I got this far and cannot finish it. Can you please help me? Thank you.
v=4/3pi*(s/4pi)**3/2
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
volume of a sphere =v=(4/3)(pie)(r^3)
surace area of a sphere=s=4(pie)(r^2)
hence their ratio is (v/s)=[(4/3)(pie)(r^3)]/[4(pie)(r^2)]=r/3...4,pie in the numerator and denominator cancel out...r^3/r^2..will give us ..r..
hence v/s=r/3...or...v=rs/3
********************************************************
ok .we have got v=rs/3..if it is required to be
written as only a function of s..we will replace r
with s using the formula
s=4*(pie)*r^2..or r^2=s/4pie...or
r=square root of [s/4pie]...substituting this for v we
get
v=(s/3)*square root of [s/4pie]..or
v=(s/6)*square root of [s/pie]..or
multiplying by squreroot of pie ..both n.r and d.r we
get
v=(s/6pie)*square root of [s*pie]..
which is the answer given in your book.if you have
given the full problem it could have been done
accordingly.hope the working is clear.
venugopal

--- devnull@algebra.com wrote:
> This is a CONFIDENTIAL message from a student in
> response to problem 18435.
> URL:
>
http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=18435
> Student: ruthmmm@comcast.net
>
======================================================
> TEXT FOLLOWS
>
> Thank you for responding, but my book says the
> answer is
> V=s(sq root s*pi)/6pi. I'm sorry, but I should have
> written out the whole problem.
> The volume V and the surface area S of a sphere of
> radius r are given by the formulas like you have
> given me. Then it says to Express V as a function of
> S.