You have to find the density of the above, irregularly shaped object: When this plastic toy is measured with a ruler, it is 7.23 cm in height, 5.20 cm wide and 2.25 cm deep. The toy is dropped into a graduated cylinder containing water to a level of 26.9 mL, and it sinks, raising the meniscus to 61.3 mL. Calculate the volume of the toy in mL. Report your answer with units and the correct number of significant digits.

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amhugueth amhugueth · Answer 1 · 2019-09-26T22:41:06+02:00

Answer:

[tex]V_{toy}=85mL[/tex]

ρ=[tex]404.706kg/m^3[/tex]

Explanation:

We know that density is equal to the mass divided of its volume

ρ[tex]=\frac{m}{V}[/tex]

According to the Archimedes Principle the volume of displaced fluid is equivalent to the volume of the immersed object.

[tex]E=mg[/tex]

E=ρ[tex]*V_{immersed}*g[/tex]

[tex]V_{immersed}=61.3mL-26.9mL=34.4mL=3.44x10^{-5}m^3[/tex]

[tex]E=(1000kg/m^3)(3.44x10^{-5} m^3)(9.81m/s^2)=0.3374N[/tex]

[tex]E=W_{object}=m*g[/tex]

[tex]m_{object}=\frac{E}{g}=\frac{0.3374N}{9.81m/s^2}=0.0344kg[/tex]

[tex]V_{object}=(7.23cm)(5.20cm)(2.25cm)=85cm^3=85mL=8.5x10^{-5}m^3[/tex]

Now, we can calculate the density of the irregularly shaped object:

ρ=[tex]\frac{m}{V}=\frac{0.0344kg}{8.5x10^{-5} m^3} =404.706kg/m^3[/tex]