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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 18.713 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 4/3Ïr^3

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Answer:

Firstly, Let's experiment this !

Experiment 1 :

159.446g - 124.966g = 34.48g

34.48g = The mass of Mineral oil.

The density of the mineral oil = M/V = 34.48g/40mL = 0.862g/cm³.

Experiment 2 :

124.966 + 18.173 = 143.139 = The mass of solid + cylinder.

124.966 + 50.952 = 175.918 = The mass of solid + cylinder + Mineral water.

175.918 - 143.139 = 32.779 = The mass of added mineral oil.

Explanation:

Now we have to find the volume of the added mineral oil using the density from experiment 1.

V = 32.779g/0.862g/cm³ = 38.02668213mL

Since we found the volume of the solid, we then have to subtract the added mineral oil volume from the total volume from experiment 1.

Volume of solid = 40-38.02668213 = 1.97331787mL

Density of solid = 18.713g/1.97331787mL = 9.483013499g/cm^3

1.97331787 = (4/3)(3.14)r³

1.97331787*(3/4)(3.14) = .4713338861

.4713338861 = r ³

r = 0.7782328425158433

r = 0.78

Now that's our final answer ! r = 0.78

mickymike92

The density of the ball bearing is 7.193 g/mL and the radius is 0.91 cm

Density is defined as the mass per unit volume of a substance.

Density = mass/volume

From the first experiment:

mass of the mineral oil = mass of cylinder after addition of mineral oil - mass of cylinder before addition of mineral oil

mass of mineral oil = 159.446 g - 124.966 g = 34.480 g

volume of mineral oil in cylinder = 40.00 mL

Density of mineral oil = 34.480 g / 40.00 mL

Density of mineral oil = 0.862 g/mL

From the second experiment:

Mass of ball bearing = 18.713 g

Mass of ball bearing and mineral oil = 50.952 g

mass of mineral oil = mass of mineral oil + ball bearing - mass of ball bearing

mass of mineral oil = 50.952 g - 18.713

mass of mineral oil = 32.239 g

volume of mineral oil = mass / density

volume of mineral oil = 32.239 g / 0.862 g/mL = 37.40 mL

volume of ball bearing = volume of mineral oil + ball bearing in cylinder - volume of mineral oil in cylinder

volume of ball bearing =  40.00 -37.40 mL = 2.60 mL

Using the formula, V = πr³ where r is radius; π = 22/7

r = ∛v/π

r = ∛(2.60/22/7)

radius, r of ball bearing = 0.91 cm

Density of ball bearing = mass / volume

Density of ball bearing = 18.713 g /2.60 mL

Density of ball bearing = 7.193 g/mL

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