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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.
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