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The barrel of a fountain pen, cylindrical in shape, is $7 cm$ long and $0.5 cm$ in diameter. A full barrel of ink in the pen can be used for writing 275 words on an average. How many words would be written using a bottle of ink containing one-fourth of a litre?

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40, 000

50, 000

20, 000

55, 000

answer is B.

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Detailed Solution

Given that a cylindrical shaped barrel is

7 cm

long,

0.5 cm

in diameter and a full barrel of ink can be used for writing 275 words.
We have the following formula,
Volume of a cylinder

= π r 2 h

D = 2 r = 0.5

r = 0.5 2

Volume of a barrel is,

= 227 × 0.25 × 0.25 × 7 = 1.375 cm 3

Volume of the ink that is in the barrel will be,

= 14 × 1 L

(1L=1000

cm 3

)

= 14 × 1000 = 250 cm 3

The total number of barrels that can be filled from the given amount of ink,

= 250 1.375

The number of words,

= 250 1.375 × 275 = 50, 000

Thus, the numbers of words are

50, 000

.
Therefore the correct option is 2.

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