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Question
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?
Solution
Let us first calculate the volume of barrel of pen that is of cylindrical shape
Consider barrel,
Since 1 cm = 10 mm
Base diameter = 5 mm = 0.5 cm
Base radius, r = 0.25 cm
Height, h = 7 cm
We know that,
Volume of a cylinder = πr2h
Volume of barrel = π(0.25)27
Volume of barrel = `22/7 xx 0.25 xx 0.25 xx 7` = 1.375 cm3
Hence, according to the question,
1.375 cm3 of ink can write 3300 words
No of words that can be written by 1 cm3 of ink = `3300/1.375` = 2400 words
1/5th of a liter = 0.2L
We know that,
1L = 1000 cm3
0.2L = 200 cm3
So, no of words that can be written by 200 cm3 = 2400(200) = 480000 words
Therefore, 1/5th of a liter ink can write 480000 words.
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