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ddd [48]
2 years ago
12

A piece of high-density Styrofoam measuring 24.0 cm by 36.0 cm by 5.0 cm floats when placed in a tub of water. When a 1.5 kg boo

k is placed on top of the Styrofoam, the Styrofoam partially sinks at 3.0 cm. Assuming that the density of water is 1.00 g/ml, what is the density of Styrofoam?
Chemistry
1 answer:
zheka24 [161]2 years ago
4 0

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) cm^{3}

                                 = 4320 cm^{3}

or,                             = 4.32 \times 10^{3} cm^{3}

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

         = 1.73 \times 10^{3} cm^{3}

Hence, mass of displaced water is as follows.

                 mass = density × volume

                           = 1.00 g/cm^{3} \times 1.73 \times 10^{3} cm^{3}

                           = 1.73 \times 10^{3} g

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

                  1.73 \times 10^{3} g = 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 = \frac{mass}{volume}  

                                 = \frac{230}{4.32 \times 10^{3} cm^{3}}

                                 = 53.24 \times 10^{-3} g cm^{-3}

Thus, we can conclude that the density of Styrofoam is 53.24 \times 10^{-3} g cm^{-3}.

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