Question

The barrel fountain pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel of ink in a pen is used up in writing 330 words. On average how many words would be used up a bottle of ink containing one-fifth of a liter?

Answer 1

Hint: First we will first divide the diameter by 2 to find the radius of the barrel and then use the formula to find the volume of the cylinder is \[\pi {r^2}h\], where \[r\] is the radius of the circle and \[h\] is the height of the cylinder to find the volume of the barrel. Then we will convert the one-fifth of a liter into centimeters to find the volume of ink in the bottle and then divide the volume of ink in the bottle by the volume of a barrel to find the total number of barrels that can be filled from a given volume of ink. Then multiply the obtained value by 330 to find the required number of words.

Complete step by step answer:

We are given that the barrel fountain pen cylindrical in shape is 7 cm long and 5 mm in diameter. A full barrel of ink in the pent is used up in writing 330 words.

Dividing the diameter by 2 to find the radius of the barrel, we get
\[
   \Rightarrow r = \dfrac{5}{2} \\
   \Rightarrow r = 0.25{\text{ cm}} \\
 \]

We know that the formula to find the volume of the cylinder is \[\pi {r^2}h\], where \[r\] is the radius of the circle and \[h\] is the height of the cylinder

Finding the volume of the barrel using the above formula, we get
\[
   \Rightarrow \pi \times {\left( {0.25} \right)^2} \times 7 \\
   \Rightarrow \pi \times 0.0625 \times 7 \\
   \Rightarrow \pi \times 0.4575 \\
 \]

Substituting the value of \[\pi \] in the above equation, we get
\[
   \Rightarrow \dfrac{{22}}{7} \times 0.4575 \\
   \Rightarrow 1.375{\text{ c}}{{\text{m}}^3} \\
 \]

We know that \[1{\text{ litre}} = 1000{\text{ c}}{{\text{m}}^3}\].

Converting the one-fifth of a liter into centimeters to find the volume of ink in the bottle, we get
\[
   \Rightarrow \dfrac{1}{5} \times {\text{liter}} \\
   \Rightarrow \dfrac{{1000}}{5} \\
   \Rightarrow 200{\text{ c}}{{\text{m}}^3} \\
 \]

Dividing the volume of ink in the bottle by volume of a barrel to find the total number of barrels that can be filled from a given volume of ink, we get
\[
   \Rightarrow \dfrac{{200}}{{1.375}} \\
   \Rightarrow 145.45 \\
 \]

Multiplying the above value by 330 to find the required number of words, we get
\[ \Rightarrow 145.45 \times 330 = 48000\]

Thus, there are 48000 numbers of required words.

Note: In solving this type of question, the key concept is to know the area of the cylinder and the volume of the cylinder. Some students forget to notice that the volume of ink in the bottle is already mentioned in this problem, you just have to convert it into centimeters, that is the only tricky part in this question.