Question

answer the following question related to density. remember significant digits. a) calculate the mass of a block of aluminum with dimensions 12 cm long, 5 cm wide, and 3 cm high. the density of aluminum is 2.70 g/cm³. b) calculate the mass of a block of copper with dimensions 150.1 cm long, 11 cm wide, and 4.9 cm high. the density of copper is 8.96 g/cm³.

Explanation:

Step1: Calculate volume of aluminum block

The volume formula for a rectangular - prism is $V = l\times w\times h$. For the aluminum block, $l = 12\ cm$, $w = 5\ cm$, $h = 3\ cm$. So $V_{aluminum}=12\times5\times3= 180\ cm^{3}$.

Step2: Calculate mass of aluminum block

The density formula is $
ho=\frac{m}{V}$, so $m=
ho\times V$. Given $
ho_{aluminum}=2.70\ g/cm^{3}$ and $V_{aluminum}=180\ cm^{3}$, then $m_{aluminum}=2.70\times180 = 486\ g$.

Step3: Calculate volume of copper block

For the copper block, $l = 150.1\ cm$, $w = 11\ cm$, $h = 4.9\ cm$. So $V_{copper}=150.1\times11\times4.9=150.1\times53.9 = 8090.39\ cm^{3}$.

Step4: Calculate mass of copper block

Given $
ho_{copper}=8.96\ g/cm^{3}$ and $V_{copper}=8090.39\ cm^{3}$, then $m_{copper}=8.96\times8090.39\approx72589\ g$ (using significant - digits rules).

Answer:

a) 486 g
b) 72589 g