Question

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is

• A. $12000\pi m{m}^3$
• B. $800\pi m{m}^3$
• C. $80000\pi m{m}^3$
• D. $120\pi m{m}^3$

Answer 1

The correct option is C $80000\pi m{m}^3$

Given, $r=100$ mm
$r+\Delta r=98$ mm
$\Rightarrow \Delta r=-2$ mm
Volume of sphere $V=\frac{4}{3}\pi r^3$
$\Rightarrow \frac{dV}{dr}=4\pi r^2$
Approximate change in volume $=dV=\left(\frac{dV}{dr}\right)\Delta r$
$=-8\pi r^2=-80000\pi$
Approximate decrease in $V=80000\pi {mm}^3$