Question

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

Answer 1

Hint: As we know that the volume of a sphere of radius ‘r’ is given by as follows:
Volume of sphere \[=\dfrac{4}{3}\pi {{r}^{3}}\].
After using the above formula we will get the volume of the capsule which is equal to the volume of medicine that is needed to fill the capsule.

Complete step-by-step answer:
We have been given the diameter of a spherical capsule to be 3.5 mm.
As we know that the volume of sphere of radius r is given as follows:
Volume of sphere \[=\dfrac{4}{3}\pi {{r}^{3}}\].
Also, we know that the radius (r) = \[=\dfrac{Diameter(D)}{2}\]
So, \[r=\dfrac{d}{2}=\dfrac{3.5mm}{2}\] for the given capsule.
Volume \[=\dfrac{4}{3}\pi {{r}^{3}}\]
\[\begin{align}
  & =\dfrac{4}{3}\pi \times {{\left( \dfrac{3.5}{2} \right)}^{3}} \\
 & =\dfrac{4}{3}\pi \times \dfrac{3.5}{2}\times \dfrac{3.5}{2}\times \dfrac{3.5}{2} \\
\end{align}\]
As we know that \[\pi =\dfrac{22}{7}\], then
\[=\dfrac{4}{3}\times \dfrac{22}{7}\times \dfrac{3.5}{2}\times \dfrac{3.5}{2}\times \dfrac{3.5}{2}=22.45m{{m}^{3}}\]
Hence, the volume of the capsule is equal to \[22.45m{{m}^{3}}\].
As we know that the volume of a capsule is equal to the volume of medicine that is needed to fill this capsule.
Therefore, the volume of medicine required to fill this capsule is equal to \[22.45m{{m}^{3}}\].

Note: Just remember the point that we have been given the diameter of the capsule but we are using the radius in the formula to calculate its volume, so change the diameter into radius first. Also, it is better to take the value of \[\pi \] as equal to \[\dfrac{22}{7}\] instead of 3.14 if nothing is mentioned in the given question. In this question, we can cancel off terms easily using the value of \[\pi =\dfrac{22}{7}\].