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