Question

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

Answer 1

Step 1: Find the volume of ink in the pen.

Given that, diameter $=5mm$

Thus, radius $r$ $=\frac{5}{2}mm$ $(Radius=\frac{Diameter}{2})$

$=0.25cm$ $(1cm=10mm)$

Height $\left(h\right)=7cm$

Volume of ink in cylindrical barrel $={\mathrm{\pi r}}^2\mathrm{h}$, where $r$ is radius and $h$ is height

$$\begin{gathered} =\frac{22}{7}\times 0.25\times 0.25\times 7 \\ =1.375c{m}^3 \end{gathered}$$

Also, $1.375c{m}^3=1.375ml$

Step 2: Find the number of words written with the help of $1ml$ of ink.

Ink used of $330words=1.375ml$

Number of words written in $1ml=\frac{330}{1.375}$

Step 3: Find the number of words that can be written with one-fifth of a liter of ink.

Number of words written in $\frac{1}{5}litre=\frac{330}{1.375}\times \frac{1}{5}\times 1000$

$=48000$

Hence, the total number of words that would use up a bottle of ink containing one-fifth of a liter is $48000$.