A capsule of medicine is in the shape of a sphere of diameter $3.5\ mm$. How much medicine (in $mm^3$) is needed to fill this capsule?

 Given:

A capsule of medicine is in the shape of a sphere of diameter $3.5\ mm$.

To do:

We have to find the volume of medicine (in $mm^3$) needed to fill the capsule.

Solution:

Diameter of the spherical medicine capsule $= 3.5\ mm$

This implies,

Radius of the spherical medicine capsule $= \frac{3.5}{2}\ mm$

$=\frac{35}{20}\ mm$

$=1.75\ mm$

Volume of the medicine needed $=\frac{4}{3} \times \frac{22}{7} \times 1.75 \times 1.75 \times 1.75$

$=\frac{88}{21} \times 5.359375$

$=22.458 \mathrm{~mm}^{3}$

Hence, 22.458 \mathrm{~mm}^{3}$ of medicine is needed to fill the capsule.