Question

A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm³ of ball bearings. Find the:

1. maximum number of ball bearings that each box can have.
2. mass of each box of ball bearings in kg.
   (Use π = `22/7`)

Answer 1

Given: Radius = 7 mm = 0.7 cm = `7/10` cm  ....(since 1 cm = 10 mm)

Volume of bearings per box = 2156 cm³

Mass of one bearing = 4 g

π = `22/7`

a. Maximum number of ball bearings:

Volume of one ball = `4/3πr^3`

= `4/3 xx 22/7 xx (7/10)^3`

No. of balls = `2156/(4/3 xx 22/7 xx (7/10)^3)`

= `(2156 xx 3 xx 10^3)/(4 xx 22 xx 7^2)`

= `(2156 xx 3000)/(4312)`

= 1500

b. Mass of each box of ball bearings:

Total mass = 1500 × 4 g

= 6000 g

= 6 kg