Question

The barrel of a fountain pen, cylinder in shape, is 7 cm long 5 mm is its diameter. A full of ink in the pen will be used when writing 310 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre?

Answer 1

Hint: First find the radius of the barrel and then use it with the given height to calculate the amount of ink in the barrel of a fountain pen. Then, calculate the number of words that can be written using 1 litre of ink. Hence, calculate the number of words that can be written using $\dfrac{1}{5}$ litre of ink.

Complete step by step solution:
We are given that the height of the barrel is 7 cm and the diameter is 5mm
We will first convert diameter into radius as the radius is half the diameter.
Then, the radius of the barrel is $\dfrac{5}{2}mm$
Since, we have height in cm, convert the unit of the radius into cm by dividing it by 10.
$\dfrac{5}{{2\left( {10} \right)}} = \dfrac{1}{4}{\text{cm}}$
We will now calculate the total volume of the barrel.
The given barrel of the fountain pen is a cylinder.
And we know that the volume of the cylinder is given by $\pi {r^2}h$, where $r$ is the radius of the cylinder and $h$ is the height of the cylinder.
Therefore the volume of ink barrel is
$
  \pi {\left( {\dfrac{1}{4}} \right)^2}\left( 7 \right) \\
   = \dfrac{{22}}{7}{\left( {\dfrac{1}{4}} \right)^2}\left( 7 \right) \\
   = \dfrac{{22}}{{16}} \\
  {\text{ = 1}}{\text{.375c}}{{\text{m}}^{\text{3}}} \\
$
Convert the volume into litres by dividing it by 1000.
$\dfrac{{1.375}}{{1000}} = 0.001375{\text{L}}$
Thus, a full ink pen has 0.001375 litres of ink.
Also, 0.01375 litres of ink can write 310 words.
So 1 Litre can write $\dfrac{{310}}{{0.001375}} = 225,454.5$ words
We have to find the words that can be written using $\dfrac{1}{5}$ Litres of ink.
So, multiply $\dfrac{1}{5}$ L with $225,454.5$
$225,454.5 \times \dfrac{1}{5} = 45,090.90 \approx 45,090$
Hence, the number of words that can be written using $\dfrac{1}{5}$ Litres of bottle of ink is 45,090 words.

Note: In these type of questions, the concept of the unitary method is used where we first find the number of letters written using 1 litre of ink and then multiply the unit value (1 litre ) with the amount of ink you want to find the total words that can be written, that is, $\dfrac{1}{5}$ litres.