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A measuring cylinder contains 50cm^3 of water. A ball is submerged in the measuring cylinder, and the water level now reads 78cm^3 The ball has a mass of 33 g. Calculate the density of the ball, giving your answer to 2 significant figures.

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A measuring cylinder contains 50cm^3 of water.
A ball is submerged in the measuring cylinder, and the water level now reads 78cm^3
The ball has a mass of 33 g.
Calculate the density of the ball, giving your answer to 2 significant figures.

A measuring cylinder contains 50cm^3 of water. A ball is submerged in the measuring cylinder, and the water level now reads 78cm^3 The ball has a mass of 33 g. Calculate the density of the ball, giving your answer to 2 significant figures.

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BellaExpert · Tutor for 3 years

Answer

<br /><br />1. From the data extracted, the change in water's volume after the ball's submersion (i.e., volume of the entity in the question which is the increase in water from <br />50 cm^3 to 78 cm^3,), is V_ball = 78 cm^3 – 50 cm^3 = 28 cm^3 .<br /><br />2. Using the mass as provided in the question, mass = 33g.<br /><br />3. Now, in conjunction with the known density calculation formula (Density =mass/volume),<br />the calculated density of the ball will be as follows: <br /><br />(ρ = mass/volume): Ρ_ball = (33g / 28 cm^3 )= 1.18 g/cm^3.<br /><br />4. For the final step, consider rounding to 2 significant figures to increase the fidelity of comparison. Thus, rounding 1.18 g/cm^3 to 2 significant figures we obtain ρ_ball = 1.2 g/cm^3.

Explain

<br /><br />From the given questions, there are two main parameters: the volume displacement of water by the ball and the mass of the ball. The difference between the two readings of water in the measuring cylinder is the volume of the ball which can be expressed as:<br /><br />V = V_final - V_initial = 78cm^3 - 50cm^3.<br /><br />The known mass of the ball is 33g.<br /><br />Density is the ratio of mass to volume. So the density will be calculated as (ρ = mass/volume).<br /><br />Given that, 1cm^3 = 1g or 1 g/cm^3, is equivalent to 1000 kg/l to 1 kg/m^3<br /><br />The final value should then be approximated to 2 significant figures/numbers to maintain the precision of value when decimally approximated.<br /><br />Apply these calculations and rules, the result will be the density of the ball in g/cm^3 with an accuracy to 2 significant figures.
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