 # The barrel of a fountain pen, cylindrical in shape,

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 pin is used up on writing 3300 words on an

average. How many words can be written in a bottle of ink containing one-fifth of a litre?

Solution:

Given, length of the barrel of a fountain pen = 7 cm

and diameter $=5 \mathrm{~mm}=\frac{5}{10} \mathrm{~cm}=\frac{1}{2} \mathrm{~cm}$

$\therefore$ Radius of the barrel $=\frac{1}{2 \times 2}=0.25 \mathrm{~cm}$

Volume of the barrel $=\pi r^{2} h$ [since, its shape is cylindrical]

$=\frac{22}{7} \times(0.25)^{2} \times 7$

$=22 \times 0.0625=1.375 \mathrm{~cm}^{3}$

Also, given volume of ink in the bottle $=\frac{1}{5}$ of litre $=\frac{1}{5} \times 1000 \mathrm{~cm}^{3}=200 \mathrm{~cm}^{3}$

Now, $1.375 \mathrm{~cm}^{3}$ ink is used for writing number of words $=3300$

$\therefore 1 \mathrm{~cm}^{3}$ ink is used for writing number of words $=\frac{3300}{1375}$

$\therefore 200 \mathrm{~cm}^{3}$ ink is used for writing number of words $=\frac{3300}{1.375} \times 200=480000$