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 $2156 \mathrm{~cm}^{3}$ of ball bearings. Find the: maximum number of ball bearings that each box can have. (use $\pi=\frac{22}{7}$ )
Explanation
To find the maximum number of ball bearings that each box can have, we need to find the volume of a single ball bearing and then divide the maximum volume of the box by the volume of a single ball bearing. The volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere. Given that the radius of each ball bearing is 7 mm, we can calculate its volume as V = (4/3) * (22/7) * 7^3 = 1436.67 mm^3. Now, we can divide the maximum volume of the box (2156 cm^3) by the volume of a single ball bearing (1436.67 mm^3) to get the maximum number of ball bearings that each box can have.
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