# 006 Weight of steel ball bearings

**Example 006**

A steel plant has to fill an order from an automobile manufacturer for 100 000 steel ball bearings 12 mm in diameter. What is the total weight of the metal required to fill this order, if steel weighs 75.5 kN/m^{3}?

**Solution 006**

Radius of one steel ball bearing

$r = 6 \, \text{ mm} = 0.006 \, \text{ m}$

$r = 6 \, \text{ mm} = 0.006 \, \text{ m}$

Volume of 100 000 steel ball bearings

$V = 100\,000 [ \, \frac{4}{3}\pi(0.006^3) \, ]$

$V = 0.0288\pi \, \text{ m}^3$

Weight of 100 000 steel balls bearings

$W = \gamma V = 75.5(0.0288\pi)$

$W = 6.8311 \, \text{ kN}$ *answer*

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