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 is used up on writing $3300$ words on average. How many words can be written in a bottle of ink containing one-fifth of a$\mathrm{liter}$?

Answer 1

Step 1: Finding the volume of the cylindrical barrel :

Given

Base diameter of barrel$=5mm=0.5cm(\sin ce1mm=\frac{1}{10}cm)$

So, radius$=\frac{0.5}{2}=0.25cm$

Height of barrel, $h=7cm$

The barrel is in a cylindrical shape. Let us calculate the volume of the barrel

Volume of a cylinder $=\pi r^{2}h$

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

Thus, the volume of the cylindrical barrel is$1.375c{m}^3$

Step 2: Find the number of words :

A full barrel of ink in the pen is used up on writing $3300$words

$1.375c{m}^3$ of ink can write$3300$ words

Number of words that can be written by $1c{m}^3$ of ink $=\frac{3300}{1.375}=2400$words

${\left(\frac{1}{5}\right)}^{th}ofaliter=0.2L$

We know that,

$\begin{array}{rcl}1L& =& 1000c{m}^3\\ & \Rightarrow & 0.2L=200c{m}^3\end{array}$

So, number of words that can be written by $200c{m}^3=2400\times \left(200\right)=480000$words

Therefore, ${\left(\frac{1}{5}\right)}^{th}ofaliter$of ink can write $480000$ words.