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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%. –  kellax Dec 30 '12 at 3:30

1 Answer 1

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. –  kellax 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. tutorial.math.lamar.edu/Classes/CalcI/Differentials.aspx. 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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