Question

7. The ball of a ballpoint pen is 1 mm in diameter and has an ASTM grain size of 10. How many grains are there in the ball

Answer 1

Given :

The ball of a ballpoint pen is 1 mm in diameter and has an ASTM grain size of 10.

To Find :

How many grains are there in the ball.

Solution :

Volume of ball is :

`V=(4\pi r^3)/(3)\\\\V=(4\pi (0.5)^3)/(3)\ mm^3\\\\V=(4* 3.14* 0.5^3)/(3)\ mm^3\\\\V=0.523\ mm^3`

Grains per unit volume is given by :

`N = 2^(n-1)* 10^3\ grains/mm^3` ( Here, n is ASTM grain size ).

Putting n = 10 , we get :

`N = 2^(10-1)* 10^3\ grains/mm^3\\\\N = 5.2* 10^5\ grains/mm^3`

Number of grains are :

`n = V* N\\\\n = 0.523* 5.2* 10^5\ grains\\\\n = 2.7196* 10^5\ grains`

Hence, this is the required solution.