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, = [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]
= [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].
