Question

A capsule of medicine is in the shape of a sphere of diameter $3.5$mm. How much medicine is needed to fill this capsule?

Answer 1

We know that the volume of sphere with radius $r$ is $V=\frac{4}{3}\pi r^3$.

It is given that the diameter of the capsule is $3.5$ mm, therefore, the radius of the capsule is$r=\frac{3.5}{2}=1.75$ mm and thus,

$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (1.75{)}^3=\frac{4}{3}\times \frac{22}{7}\times 5.35=22.45$ mm${}^3$

Hence, $22.45$ mm${}^3$ of medicine is needed to fill the capsule.