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.
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.
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.