Question

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre?

Answer 1

Height of the barrel = h = 7 cm
Radius of the barrel = r = 2.5 mm = 0.25 cm
Volume of the barrel = $\mathrm{\pi }{r}^{\mathit{2}}h$
$$\begin{gathered} =\frac{22}{7}\times 0.25\times 0.25\times 7 \\ =22\times 0.25\times 0.25 \\ =1.375{\mathrm{cm}}^3 \end{gathered}$$

i.e., 1.375 cm³ of ink is used for writing 330 words
Now, number of words that could be written with one-fifth of a litre, i.e., $\frac{1}{5}\times 1000$ cm³ = $330\times \frac{1}{1.375}\times \frac{1}{5}\times 1000=48000$
∴ 48000 words would use up a bottle of ink containing one-fifith of a litre.