Question

A graduated cylinder is filled to the 40.00−mL mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g, respectively. In a separate experiment, a metal ball bearing of mass 21.867 g is placed in the cylinder and the cylinder is again filled to the 40.00−mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density and radius of the ball bearing (volume of a sphere of radius r is 4/3πr3).

Answer 1

From 1st experiment,
volume of mineral oil = 40 mL
mass of mineral oil = 159.446 g - 124.966 g = 34.48 g
So, density of mineral oil = mass/ volume
                                                     = 34.48 g / 40 mL
                                                     = 0.862 g/mL   <------Answer

From expriment 2:
mass of ball = 21.867 g
combined mass = 50.952 g

So,
mass of mineral oil = 50.952 - 21.867 = 29.085 g
since density of mineral oil = 0.862 g/mL
Volume of oil = mass / density
                              = 29.085 / 0.862
                              =33.741 mL

Total volume = 40 mL
Volume of ball = 40 - 33.741 = 6.259 mL
                                 =6.259 cm^3

Volume = (4/3)*pi*r^3
6.259 = (4/3)*pi* r^3
r=1.143 cm
Radius is 1.143 cm <-----Answer