Question

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?

Answer 1

$\boxed{ \boxed{ \overline {\underline{ \bf \red{SOLUTION \: ☻}}}}}$

$\rm \: Given, \: height \: of \: cylindrical \: pen = 7 \: cm$

$\rm\: Radius = \frac{Diameter}{2} = \frac{0.5}{2} \: cm$

$\therefore \: \rm \: Volume \: of \: barrel \: of \: a \: fountain \: pen = \pi r {}^{2} h$

$\rm = \frac{22}{7} \times \bigg( \frac{0.5}{2} \bigg) {}^{2} \times 7$

$\rm = \frac{22}{7} \: cm {}^{3}$

$\rm \: It \: is \: given \: that, \: a \: pen \: can \: write \: 275 \: words \: by \: using \: the \: ink \: \frac{22}{16} \: cm {}^{3} .$

$\rm \: \therefore \: \: Volume \: of \: in = 275 \: words$

$\longrightarrow \: \: \rm \: \frac{22}{16} \: cm {}^{3} = 275 \: words$

$\longrightarrow \: \rm \frac{1}{4} \times 1000 \: cm {}^{3} = \frac{275 \times 16}{22} \times \frac{1}{4} \times 1000$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm = \: \red{50000}$

$\rm \because \: [he \: will \: use \: \frac{1}{4} \: L \: of \: ink \: to \: write \: words]$

$\rm \: Hence, \: the \: pen \: can \: write \: \underline {\underline{\red{50000}} }\: words \: by \: \boxed{\red{\frac{1}{4}}} \: L \: of \: ink.$