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I have the following function:

$$ u(r)= \frac{4}{3} \pi r^{3} $$

I need to calculate the % change of volume of the sphere using differential if I increase the radius by 1% (0.01).

Can anyone help me here, I'm clueless how to solve this.

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Given the suggested approach, the obvious first steps are to try and answer the questions "what is the differential?" and "How does the differential measure change?" – Hurkyl Dec 30 '12 at 3:20
With help of differential i need to calculate by how much % does the volume of the shpere change if I increase the radius by 1%. – Sterling Duchess Dec 30 '12 at 3:30

Consider some function $f(x)$. Let's say you know $f(x)$ and you want to evaluate $f(x+\Delta x)$. For small changes in $x$, we can approximate the $\Delta f$ as follows:

$\Delta f=f(x+\Delta x)-f(x)\approx f^{\prime}(x)\Delta x=df$

$df$ is the differential. For your case, your function is the volume and you are changing the radius($r$) by a small amount. So understand and use the above definition to do your calculation.

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Thanks, means a lot but it dosent help me i couldnt atend the class when they were doing this so now im clules. – Sterling Duchess Dec 30 '12 at 3:42
This was asked by @miha, but Kellax seems more concerned about it? Something seems fishy. – Calvin Lin Dec 30 '12 at 3:50
@kellax: then please flag it and ask a moderator to combine the accounts. Helps you with reputation, helps the rest of us with lack of confusion. – Ross Millikan Dec 30 '12 at 3:56
@kellax here is a link to a tutorial on differentials. Do the examples. This should help. How much of single variable calculus do you know? Ask more if things are not clear. Be specific with what you don't understand. – abiyo Dec 30 '12 at 5:23

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