Question

1. a rectangular solid of unknown density is 5 meters long, 4 meters wide, and 2 meters high. the mass of this solid is 300 grams. given this information for this homogeneous material, calculate the density.
2. a rock occupies a volume of 20 cm³ and has a mass of 54 g. find the density of this rock.

Explanation:

Step1: Calculate volume of rectangular solid

The volume formula for a rectangular solid is $V = l\times w\times h$. Given $l = 5$ m, $w = 4$ m, $h = 2$ m. So $V=5\times4\times2= 40$ $m^{3}$. Since $1$ $m^{3}=10^{6}$ $cm^{3}$, then $V = 40\times10^{6}$ $cm^{3}$.

Step2: Calculate density of rectangular - solid material

The density formula is $
ho=\frac{m}{V}$. Given $m = 300$ g and $V = 40\times10^{6}$ $cm^{3}$, so $
ho=\frac{300}{40\times10^{6}}=7.5\times10^{-6}$ g/$cm^{3}$.

Step3: Calculate density of rock

Given $m_{rock}=54$ g and $V_{rock}=20$ $cm^{3}$, using the density formula $
ho_{rock}=\frac{m_{rock}}{V_{rock}}$. Then $
ho_{rock}=\frac{54}{20}=2.7$ g/$cm^{3}$.

Answer:

The density of the homogeneous material of the rectangular solid is $7.5\times10^{-6}$ g/$cm^{3}$ and the density of the rock is 2.7 g/$cm^{3}$.