Question

1. A 25 g rock is placed in a graduated cylinder with water. The volume of the liquid rises from 18.3 mL to 21.4 mL Calculate the density of the rock in g/cm^3.
2. The density of aluminum is 2.7 g/mL If the length and width of a 1.08 kg. Al bar are 5 cm x 8 cm, then what is the height of the Al bar?

Answer 1

Answer:

1. $\rho=8.06g/cm^3$

2. $H=10cm$

Explanation:

Hello,

1. In this case, since the volume of the rock is obtained via the difference between the volume of the cylinder with the water and the rock and the volume of the cylinder with the water only:

$V=21.4mL-18.3mL=3.1mL$

Thus, the density turns out:

$\rho=\frac{m}{V}=\frac{25g}{3.1cm^3} \\\\\rho=8.06g/cm^3$

2. In this case, given the density and mass of aluminum we can compute its volume as follows:

$V=\frac{m}{\rho}=\frac{1080g}{2.7g/cm^3}=400cm^3$

Moreover, as the volume is also defined in terms of width, height and length:

$V=W*H*L$

The height is computed to be:

$H=\frac{V}{L*W}=\frac{400cm^3}{5cm*8cm}\\ \\H=10cm$

Best regards.