A graduated cylinder is filled to the 40.00-mL mark with a mineral oil. The mass

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 19.532 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 4/3 pi r^3). g/cm^3 cm

Explanation / Answer

Volume of cylinder = 40.0 ml

Mass if cylinder (c) = 124.966 g

Mass of cylinder + mass of mineral oil (m) = 159.446

Mass of mineral oil (m) = 34.48 g

Density of oil = 34.48/ 40 = 0.862 g/ml

Mass of ball + mass of oil = 50.952 g

Since mass of ball = 19.532 g ( given)

Therefore mass of oil in cylinder = 31.42 g

So volume of oil present in cylinder = mass / density = 31.42 / 0.862 = 36.45 ml

Therefore volume of ball = 40 - 36.45 = 3.55 ml.

Density of ball = mass / volume = 19.532/ 3.55 = 5.5019 g/ml

Volume of ball = 4/3 r³

3.55 = 4/3 r³

r = 0.946487 cm

1cm³ = 1ml and = 3.14

Final answer of question is

Density of ball = 5.5019 g/ cm³

Radius of ball = .0946487 cm

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