A barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. If a filled barrel is used up on writing 330 words on an average, how many words would use up a bottle of ink containing 1/5th of a litre of ink?

Here, for the fountain pen
Height (h) = 7 cm
Diameter = 5 mm
  = 0.5 cm
Radius (r) = $\frac{0.5}{2}cm$
  = 0.25 cm

Now, use the formula for the volume of the cylinder. So,
$$\begin{gathered} Volume of the barrel of the pen={\mathrm{\pi r}}^2\mathrm{h} \\ = \frac{22}{7}\times 0.25\times 0.25\times 7 \\ = 1.38 {\mathrm{cm}}^3 \end{gathered}$$

Next,
Volume of the ink to be consumed = $\left(\frac{1}{5}\right)\left(1\right)l$
        $$\begin{gathered} =\left(\frac{1}{5}\right)\left(1000\right) c{m}^3 \\ =200 c{m}^3 \end{gathered}$$
Now,
Number of words that can be written consuming 1.38 cm³ of ink = 330
Number of words  that can be written using 200 cm³ of ink = $\frac{330}{1.38}\left(200\right)$
  = 47826

Therefore, 47826 words would use up a bottle of ink containing 1/5th of a litre of ink