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Q.

The barrel of a fountain pen, cylindrical in shape, 7cm long and 5mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of litre?

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a

60000

b

66000

c

48000

d

50000

answer is C.

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Detailed Solution

Given, a barrel of a fountain pen is cylindrical in shape. It is 7cm long and 5mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words. We have to find the number of words to be written to use up a bottle of ink containing one fifth of litre.
Since the barrel is in cylindrical shape so we can draw the figure as-

https://www.vedantu.com/question-sets/deedc841-00e0-42fa-a2bb-fd5f86112d786809343328131979319.png

First we will find the volume of the cylindrical barrel. We know that the volume of cylinder is given as-
⇒ Volume of cylindrical barrel

= π r 2 h

, where r = radius and h = height
Now, according to the figure h = 7cm and diameter = 5mm
We know that

1 m m = 110 c m

so diameter

= 510 c m

Now we know that r = half of the diameter.

⇒ r = 510 × 12

On solving, we get-

⇒ r = 14 c m

We also know that

π = 227

On putting the given values in the formula, we get-
⇒Volume of cylindrical barrel

= 227 × 142 × 7

On solving, we get-
⇒ Volume of cylindrical barrel

= 118 = 1.375 c m 3

………….(1)
We know that 1 Litre

= 1000 c m 3

Then the given volume of ink in the bottle

= 15 × 1000 c m 3 = 200 c m 3

………..(2)
This means that

1.375 c m 3

ink is used in writing the number of words = 330
So

1 c m 3

ink is used to write the number of words

= 330 1.375

So

200 c m 3

ink is used to write the number of words

= 330 1.375 × 200 = 48000

⇒

200 c m 3

ink is used to write the number of words = 48000

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