Question

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 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)

Answer 1

Given:

The barrel is cylindrical

Length h = 7h 

Diameter = 5cm

⇒ Radius r = 0.25r cm

One full barrel writes 310 words

The bottle contains 15

Step 1: Volume of ink in one full barrel

Vbarrel​ = πr2h = π(0.25)2 × 7

= π × 0.0625 × 7 = 0.4375π cm3

Using π = `22/7`

Vbarrel ​= 0.4375 × `22/7` = 1.375 cm³

Step 2: Volume of ink in the bottle

`1/5` Litre = 200 cm³

Step 3: Number of barrels the bottle can fill

Number of barrels = `200/1.375`

= 145.45

Step 4: Total number of words

Total words = 145.45 × 310

= 45,091

Step 5: Nearest 100 words

45, 100 words