# Calculating volume change of sphere with differential

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.