Question

The barrel of a fountain pen , cylindrical in shape,is 7cm long and 5mm in diameter.A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre? Answer correct to nearest 100 words .

Answer 1

$\mathfrak{Heya \: mate.\: Solution\: below.}$
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★$<b>Volume of Cylinders</b>$★

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$<font color = "red">Answer - </font color>$


• Firstly,

one-fifth of a litre

$= \frac{1}{5} \times 1 \: l$

$= \frac{1}{5} \: l$

$= \frac{1}{5} \times 1000 \: {cm}^{3}$

$= 200 \: {cm}^{3}$

•°• One-fifth of a Litre = 200 cm³




• Now, Given length (height) of the cylindrical barrel = 7 cm



• Given diameter of the barrel = 5 mm = 5/10 cm


=> Radius of the barrel,

$= \frac{d}{2}$

$= \frac{ \frac{5}{10} }{2}$

$= \frac{5}{20}$

= 5/20 cm.




• Then, Volume of a full barrel

$= \pi {r}^{2} h$

$= \frac{22}{7} \times \frac{5}{20} \times \frac{5}{20} \times 7$

$= 22 \times \frac{1}{4} \times \frac{1}{4}$

$= \frac{11}{8}$

= 11/8 cm³.





• Now, 11/8 cm³ of ink is required to write 310 words.

• Then, 1 cm³ of ink would be required to write -

$= 310 \times \frac{8}{11} \: words$

$= \frac{2480}{11} \: words$

$= 225.4545 \: words$



• Then, one-fifth of a litre, i.e. 200 cm³ of ink would be required to write -

$= 225.4545 \times 200 \: words$

$= 45090.9090 \: words$

= 45090.9090

≈ 45100 words... (rounded to the nearest hundred)



♥ ♥ ♥ •°•$<font color ="blue"> 45100 words would use up one-fifth of a Litre of ink.</font color>$ ♥ ♥ ♥
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$<marquee>Thank you.. (^_-).$