Question

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the cylindrical part of the capsule is 14mm and the diameter of the hemisphere is 6mm, then find the volume of the medicine capsule.

Answer 1

Hint: The medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the cylindrical part of the capsule and the diameter of the hemispheres are given. The volume of a cylinder having length h and radius r is given by $\pi {{r}^{2}}h$. Again , volume of a hemisphere with radius r is given by $\dfrac{2}{3}\pi {{r}^{3}}$ .
Find the individual volumes of the cylinder and the hemispheres using these formulae.
Now, note that the total volume of the capsule is the sum of the volumes of the cylinder and the hemispheres.

Complete step-by-step solution:

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends.
The length of the cylindrical part of the capsule is 14mm, and the diameter of hemisphere is 6mm.
Therefore the total volume of the capsule is the sum of the volumes of the cylinder and the hemispheres.
The cylindrical part of the capsule has length 14mm and radius $\dfrac{6}{2}=3$mm.
We know, the volume of a cylinder having length h and radius r is given by $\pi {{r}^{2}}h$
∴ Applying the formula we find the volume of the cylinder as $\text{ }\!\!\pi\!\!\text{ }\!\!\times\!\!\text{ (3}{{\text{)}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ 14=126 }\!\!\pi\!\!\text{ =396m}{{\text{m}}^{3}}$ (taking π=22/7)
Again we know, volume of a hemisphere with radius r is given by $\dfrac{2}{3}\pi {{r}^{3}}$
The volume of each hemisphere with radius 3mm will be $\dfrac{2}{3}\pi {{\left( 3 \right)}^{3}}=\dfrac{2}{3}\times \pi \times 27=18\pi =56.52\text{m}{{\text{m}}^{3}}$ Therefore the total volume of the capsule is = volumes of the cylinder + volume of two hemispheres, i.e.
$\begin{align}
  & 396+\left( 2\times 56.52 \right) \\
 & =396+113.04 \\
 & =509.04m{{m}^{3}} \\
\end{align}$
Hence, the volume of the medicine capsule is $509.04m{{m}^{3}}$.

Note:
Note the formulae of finding the volume of the following figures.

Figure	Volume
Cube	$a^3$
Cuboid	$l\times b\times h$
Sphere	$\dfrac{4}{3}\pi {{r}^{3}}$
Hemisphere	$\dfrac{2}{3}\pi {{r}^{3}}$
Cylinder	$\pi {{r}^{2}}h$
Cone	$\dfrac{1}{3}\pi {{r}^{2}}h$ .