1) First of all, let's calculate the radius r of the ball-bearing. We know the value of the circumference:
[tex]c=2\pi r = 45.1~mm=4.51~cm[/tex]
From this, we can find the radius:
[tex]r= \frac{c}{2 \pi} = \frac{4.51~cm}{2 \pi}=0.72~cm [/tex]
2) Now, let's find the volume:
[tex]V= \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.72~cm)^3 = 1.56~cm^3[/tex]
3) Finally, we can calculate the density. We know the mass, [tex]m=11.6~g[/tex], therefore we have
[tex]d= \frac{m}{V}= \frac{11.6~g}{1.56~cm^3}=7.44~g/cm^3 [/tex]
