Find the number of steel ball bearings, each of the diameter 0.7 cm, that can be made from 1 kg steel, given that 1 cm (cube) of steel weighs 7.85 g.

Question

Find the number of steel ball bearings, each of the diameter 0.7 cm, that can be made from 1 kg steel, given that 1 cm³ of steel weighs 7.85 g.

Answer 1

Steel bearing is a sphere, volume: V = 4/3 π (r^3). If diameter is 0.7 cm, then radius, r = 0.35 cm. 

V= 4/3 x 3.4 x(0.35)^3 = 0.18 cm^3. The weight then will be 0.18 x 7.85 g = 1.413 g/one bearing. Total amount of bearings: 1kg = 1000 g/1.413 = 707.7, or 707 bearings. We must round up down as there is not enough material make another bearing.