The densities of cork, lead, and water are 0.240, 11.34, and 0.997 g/cm3 at 25°c, respectively. if 20.0 grams of lead are placed inside an 85.0 cm3 piece of cork, what is the overall density and will it float on water?

overall density = 0.475 g/cm³
Conclusion: if will float on water

Explanation:

1) name the variables:

masa = m
volume = v
density = d

2) Formula

d = m / v ⇒ m = v × d ⇒ v = m / d

3) Solution

i) Calculate the mass of the cork

V cork = 85.0 cm³ ⇒ m = 85.0 cm³ × 0.240 g / cm³ = 20.4 g

ii) Mass of lead + cork

m = 20.0 g + 20.4 g = 40.4 g

iii) Volume of the cork and lead

Assume that, since the lead is inside the cork, the total volume is the same volume of the cork: 85.0 cm³ (any how the contribution of the lead to the volumen is so small that it does not affect the results).

iv) Calculate the overall density

d = 40.4 g / 85.0cm³ = 0.475 g/cm³

4) Conclusion:

Since the overall density  is less than the density of water, the object will float.

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