Question

questions 10 and 11 refer to the following:
the diagrams below represent three samples of the same substance, each having a different size and shape. the diagrams are not

1. what is the density of sample a?

a) ( 4.0 mathrm{~g} / mathrm{cm}^{3} ) b) ( 2.0 mathrm{~g} / mathrm{cm}^{3} ) c) ( 3.0 mathrm{~g} / mathrm{cm}^{3} ) d) ( 0.33 mathrm{~g} / mathrm{cm}^{3} )

1. which order of letters ranks the samples by volume from largest to smallest?

a) ( c, b, a ) b) ( a, c, b ) c) ( a, b, c ) d) ( c, a, b )

Explanation:

Step1: Calculate the volume of sample A

The volume \( V \) of a rectangular prism (sample A) is given by \( V = l\times w\times h \). Here, \( l = 2\ cm\), \( w=2\ cm\), \( h = 2\ cm\). So \( V=2\times2\times2=\ 8\ cm^{3}\).

Step2: Calculate the density of sample A

The formula for density \(
ho=\frac{m}{V}\). Given \( m = 24\ g\) and \( V = 8\ cm^{3}\), then \(
ho=\frac{24}{8}=3.0\ g/cm^{3}\).

Step3: Calculate the volume of sample B

Using the formula \( V=\frac{m}{
ho}\). Since \(
ho = 3\ g/cm^{3}\) (density of B), and from \(
ho=\frac{m}{V}\), we can also use \( V=l\times w\times h\). But using \(
ho=\frac{m}{V}\) in another way: assume \( m=
ho V\). Also, since \(
ho = 3\ g/cm^{3}\) (same substance as A and C in terms of density property, but let's calculate via dimensions. \( V=l\times w\times h=3\times2\times1 = 6\ cm^{3}\)

Step4: Compare volumes

Sample A has \( V_A=8\ cm^{3}\), sample B has \( V_B = 6\ cm^{3}\), sample C has \( V_C=12\ cm^{3}\)

Answer:

1. C. \(3.0\ g/cm^{3}\)
2. A. \(C,B,A\)