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 maximum of 2156 cm3 of ball bearings. Find the :
(a) maximum number of ball bearings that each box can have.
(b) mass of each box of ball bearings in kg.
$\Big(\text{use } \pi = \frac{22}{7}\Big)$
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(a) Given,
Radius of ball bearings = 7 mm
Volume of box = 2156 cm3 = 2156 × 103 mm3
Number of ball bearings that each box can have (N)
= $\frac{\text{Volume of box}}{\text{Volume of each ball}}$
Substituting values we get :
$$\begin{aligned}N = \frac{2156 \times 10^3}{\frac{4}{3} \times \frac{22}{7} \times 7^3} \\[1em] = \frac{2156 \times 10^3}{\frac{88}{3} \times 7^2} \\[1em] = \frac{2156 \times 3 \times 1000}{88 \times 49} \\[1em] = \frac{6468000}{4312} \\[1em] = 1500.\end{aligned}$$
Hence, maximum no. of ball bearings in a box = 1500.
(b) Mass of each box = No. of balls × Mass of each ball
= 1500 × 4 gm
= 6000 gm
= $\frac{6000}{1000}$ = 6 kg.
Hence, mass of each box = 6 kg.