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    difficult indices question

    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

    I'm stuck on this question... I write out similar base units and stuff but it doesn't seem to work, any help on the steps I should take to tackle this question?

    The answer to part a) -
    S=2^2/3 3^2/3 π^1/3 V^2/3
    I know the answer as its written on the book but I don't know the steps involved

    Thanks.
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    Quote Originally Posted by david18 View Post
    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

    I'm stuck on this question... I write out similar base units and stuff but it doesn't seem to work, any help on the steps I should take to tackle this question?

    The answer to part a) -
    S=2^2/3 3^2/3 π^1/3 V^2/3
    I know the answer as its written on the book but I don't know the steps involved

    Thanks.
    V = \frac{4}{3} \pi r^3
    and
    S = 4 \pi r^2

    The only commonality between these is r. (Well, there's a \pi, too , if you want to be technical.) So solve one of your equations for r:
    S = 4 \pi r^2

    r^2 = \frac{S}{4 \pi}

    r = \sqrt{\frac{S}{4 \pi}}

    Thus
    V = \frac{4}{3} \pi \left ( \sqrt{\frac{S}{4 \pi}} \right ) ^3

    Just because I have a love/hate thing going for radicals at the moment, I'm going to square both sides of this to get rid of it:
    V^2 = \left ( \frac{4}{3} \pi \right ) ^2 \left ( \frac{S}{4 \pi} \right ) ^3

    V^2 = \frac{16}{9} \pi ^2 \cdot  \frac{S^3}{64 \pi ^3}

    V^2 = \frac{S^3}{36 \pi }

    Can you take things from here?

    -Dan
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