Question

The radius of a sphere shrinks from $10$ to $9.8cm$. Find approximately the decrease in its volume.

Answer 1

Let $x$ be the radius and $y$ be the volume. They, $y=\frac{4}{3}\pi x^3$
Now, $y=\frac{4}{3}\pi x^3\Rightarrow \frac{dy}{dx}=4\pi x^2\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=10}=400\pi$
$\therefore dy=\frac{dy}{dx}dx\Rightarrow dy=400\pi (-0.2)=-80\pi$
$\therefore \Delta y=dy=-80\pi$