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 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 the nearest 100 words.

Height of cylindrical barrel of a pen = 7 cm.

Diameter = 5 mm = 0.5 cm. (As 10 mm = 1 cm)

Radius = $\dfrac{\text{Diameter}}{2} = \dfrac{0.5}{2} = 0.25$ cm.

Volume of cylinder = πr²h.

Putting values we get,

$\text{Volume of barrel } = \dfrac{22}{7} \times (0.25)^2 \times 7 \\[1em] = 22 \times 0.0625 \\[1em] = 1.375 \text{ cm}^3.$

Ink in the bottle = One-fifth of a litre = $\dfrac{1}{5}$ x 1000 ml = 200 ml.

Since 1 ml = 1 cm³.

∴ 200 ml = 200 cm³.

Number of words written using 1.375 cm³ (full barrel) of ink = 310.

Number of words written using 200 cm³ (bottle) of ink = $\dfrac{\text{Volume of bottle}}{\text{Volume of barrel}} \times \text{Total words}$.

= $\dfrac{200}{1.375} \times 310$ = 145.45 × 310 = 45090.90

Rounding off to nearest 100 words = 45,100.

Hence, 45,100 words use a bottle of ink containing one-fifth litre of ink.