The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter.
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?

Solution:

Height of the barrel = = 7 cm
Radius of the barrel = = 2.5 mm = 0.25 cm

Volume of the barrel $=\pi r^{2} h$

$=\frac{22}{7} \times 0.25 \times 0.25 \times 7$

$=22 \times 0.25 \times 0.25$

$=1.375 \mathrm{~cm}^{3}$

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., $\frac{1}{5} \times 1000 \mathrm{~cm}^{3}=330 \times \frac{1}{1.375} \times \frac{1}{5} \times 1000=48000$

∴ 48000 words would use up a bottle of ink containing one-fifith of a litre.  

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