Respuesta :
Explanation:
The given data is as follows.
     Width of Styrofoam = 24.0 cm
     Length of Styrofoam = 36.0 cm
     Height of Styrofoam = 5.0 cm
Therefore, volume of the Styrofoam will be calculated as follows.
         Volume = length × width × height
                =  (36.0 × 24.0 × 5.0) [tex]cm^{3}[/tex]
                 = 4320 [tex]cm^{3}[/tex]
or, Â Â Â Â Â Â Â Â Â Â Â Â Â Â = [tex]4.32 \times 10^{3} cm^{3}[/tex]
As Styrofoam partially sinks at 3.0 cm and total height of Styrofoam is 5.0 cm. Hence, height of Styrofoam above the water is (5.0 - 3 cm) = 2 cm.
So, volume of water displaced is as follows.
     24.0 cm × 36.0 cm × 2.0 cm
     = [tex]1.73 \times 10^{3} cm^{3}[/tex]
Hence, mass of displaced water is as follows.
         mass = density × volume
              = [tex]1.00 g/cm^{3} \times 1.73 \times 10^{3} cm^{3}[/tex]
              = [tex]1.73 \times 10^{3} g[/tex]
Since, book is placed on the Styrofoam. Therefore, mass of water displaced is also equal to the following.
       Mass of water displaced = mass of book + mass of Styrofoam
         [tex]1.73 \times 10^{3} g[/tex] = 1500 g + mass of Styrofoam
          (1730 - 1500) g = mass of Styrofoam
          mass of Styrofoam = 230 g
Therefore, calculate the density of Styrofoam as follows.
          Density = [tex]\frac{mass}{volume}[/tex] Â
                 = [tex]\frac{230}{4.32 \times 10^{3} cm^{3}}[/tex]
                 = [tex]53.24 \times 10^{-3} g cm^{-3}[/tex]
Thus, we can conclude that the density of Styrofoam is [tex]53.24 \times 10^{-3} g cm^{-3}[/tex].
