Answer:
The ice occupies a volume of 1.196 liters at -10 ºC.
Explanation:
We must remember that density ([tex]\rho[/tex]), measured in grams per cubic centimeters, is the ratio of mass ([tex]m[/tex]), measured in grams, to occupied volume ([tex]V[/tex]), measured in cubic centimeters, that is:
[tex]\rho = \frac{m}{V}[/tex]
We clear the mass within the formula:
[tex]m = \rho\cdot V[/tex]
The mass of the water inside the soft-drink bottle is: ([tex]\rho = 0.997\,\frac{g}{cm^{3}}[/tex] and [tex]V = 1100\,cm^{3}[/tex])
[tex]m =\left(0.997\,\frac{g}{cm^{3}} \right)\cdot (1100\,cm^{3})[/tex]
[tex]m = 1096.7\,g[/tex]
There are 1096.7 grams of water filling the soft-drink bottle completely.
Then, the water is frozen to -10 ºC and transformed into ice, the volume occupied by the ice which we can deduct from definition of density. That is:
[tex]V = \frac{m}{\rho}[/tex]
The volume occupied by the ice inside the soft-drink bottle is: ([tex]m = 1096.7\,g[/tex] and [tex]\rho = 0.917\,\frac{g}{cm^{3}}[/tex])
[tex]V = \frac{1096.7\,g}{0.917\,\frac{g}{cm^{3}} }[/tex]
[tex]V = 1195.965\,cm^{3}\,(1.196\,L)[/tex]
The ice occupies a volume of 1.196 liters at -10 ºC.
