A fountain-pen barrel is a cylinder of length 7 cm and diameter 5 mm. A full barrel writes 3300 words on average. How many words can be written with a bottle containing \(\dfrac15\) litre of ink?
4,80,000 words
Step 1: Convert diameter into radius in cm.
Diameter of barrel = 5 mm = 0.5 cm. Radius = Diameter ÷ 2 = 0.5 ÷ 2 = 0.25 cm.
Step 2: Write the formula for volume of a cylinder.
Volume of cylinder = \(\pi r^2 h\)
Step 3: Substitute values.
\(r = 0.25\,\text{cm},\; h = 7\,\text{cm}\)
Volume = \(3.1416 \times (0.25)^2 \times 7\)
= \(3.1416 \times 0.0625 \times 7 = 1.375\,\text{cm}^3\)
Step 4: Find words written per cm³ of ink.
A full barrel (1.375 cm³) writes 3300 words.
So, words per cm³ = \(3300 \div 1.375 = 2400\,\text{words/cm}^3\)
Step 5: Convert given ink volume to cm³.
\(\dfrac{1}{5}\) litre = 0.2 litre. 1 litre = 1000 cm³. So, 0.2 litre = 200 cm³.
Step 6: Find total words from 200 cm³.
Total words = (200 cm³) × (2400 words/cm³) = 480000 words.
Final Answer: 4,80,000 words