Question

A fountain pen with a cylindrical barrel of diameter 3 cm and height 14 cm filled with ink can write 3600 words. How many words can be written with that pen using 220ml of ink? (Take 1cc=1ml)
A. 6000
B. 5000
C. 7000
D. 8000

Answer 1

Hint: In this problem, first obtain the volume of the cylindrical barrel in terms of ml. Then, find the number of words written by 220 ml of ink.

Complete step by step answer:

The formula for the volume V of a cylinder having diameter d and height h is shown below.
\[
  \,\,\,\,\,\,V = \pi {r^2}h \\
   \Rightarrow V = \dfrac{\pi }{4}{d^2}h\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {r = \dfrac{d}{2}} \right) \\
\]
Now, substitute, 3 for d and 14 for h in above formula, to obtain the volume of the cylindrical barrel.
\[
  \,\,\,\,\,V = \dfrac{\pi }{4}{\left( 3 \right)^2}\left( {14} \right) \\
   \Rightarrow V = \dfrac{\pi }{4}\left( 9 \right)\left( {14} \right) \\
   \Rightarrow V = \dfrac{{126\pi }}{4} \\
   \Rightarrow V = \dfrac{{126}}{4} \times \dfrac{{22}}{7}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\pi = \dfrac{{22}}{7}} \right) \\
   \Rightarrow V = 99c{m^3} \\
\]
Since, 1cc=1ml, the volume of the cylindrical barrel is 99ml.
Now, 99 ml ink can write 3600 words, the number of words written by 220 ml of ink is calculated as follows:
\[
  \,\,\,\,\,99ml = 3600words \\
   \Rightarrow 1ml = \dfrac{{3600}}{{99}}words \\
   \Rightarrow 220ml = \dfrac{{3600}}{{99}} \times 220words \\
   \Rightarrow 220ml = 8000words \\
\]

Thus, 220 ml of ink can write 8000 words.

Note: One millimeter is equal to 1 cubic centimeter. 1cc and 1mm represents the same amount of volume in different units. The formula for the volume of the cylinder in terms of diameter is \[V = \dfrac{\pi }{4}{d^2}h\], here d is diameter and h is the height of the cylinder.