# Find the ratio of Surface area$^3$ and volume$^2$ of an sphere

IF surface are and volume of a sphere are S and V respectively,then value of $$\dfrac {S^3}{V^2}$$

a) $32$ unit; b) $9$ unit; c)$18$ unit ; d)$27$ unit;

I know the formula $S=4\pi r^2$ and $V=\dfrac43\cdot\pi r^3$.I tried to solve it and my answer is $36\pi$ which seems to nowhere of any option.

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Something doesn't jibe here: why are the choices given in "units"? If the ratio is written as intended, the $36 \pi$ should have no units. – RecklessReckoner May 16 '13 at 22:01
I dont know it was asked question and I didn't get right answer thats why I am asking.okay no units find out only number – iostream007 May 16 '13 at 22:09
Your $36\pi$ is correct for the ratio in the body of the question. – Ross Millikan May 16 '13 at 22:14
Yes, the issue is that there is apparently something missing or written down incorrectly, because the choices makes no sense... – RecklessReckoner May 16 '13 at 22:15
why are you just behind the unit @RecklessReckoner please get the number.and I've double checked the question – iostream007 May 16 '13 at 22:16

## 2 Answers

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

$$S^3/V^2=\frac{(4\pi r^2)^3}{(\frac{4}{3}\pi r^3)^2}=\frac{64\pi^3r^6}{\frac{16\pi^2r^6}{9}}=36\pi$$

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Squaring a pie gives a cubical pie!? – DJohnM May 16 '13 at 22:07
In denominator there is $4^2$ so it will $16$ not $64$ and same as for 3 – iostream007 May 16 '13 at 22:11
So $3^2$ is 27?! – RecklessReckoner May 16 '13 at 22:13
no there should be 9 – iostream007 May 16 '13 at 22:13
So now that we are all in agreement... there is something suspect about the problem statement. – RecklessReckoner May 16 '13 at 22:14

Your expression for the ratio is wrong, the ratio, $R$ is simply: $R=S/V=3/r$, which you cannot find without $r$. But if you want to find $S^3/V^2=36 \pi$, see the other answer. Like the comments said, there is something wrong in the options you were given as possible answers

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It is not an equation.and r is canceled out in expression please check it – iostream007 May 16 '13 at 22:08
Thanks! I meant expression, and by mistake I named the ratio $r$, same way as the radius. Corrected. – Wolphram jonny May 16 '13 at 22:10
what is wrong with my answer? why the negative vote? (the original question had the ratio, without exponents in the title) – Wolphram jonny May 16 '13 at 22:21
downvoter please leave the comment – iostream007 May 16 '13 at 22:22