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zhenek [66]
3 years ago
14

If the diameter of the black marble is 3.0 cm, and by using the formula for volume, what is a good approximation of its volume?

Record to the ones place.
______cm3
Determine the initial volume of water in the graduated cylinder. If you added the black marble to the graduated cylinder and it sinks, what final volume should the water level indicate? Record to the ones place.
______ML

Physics
2 answers:
Mkey [24]3 years ago
7 0

1. Answer: 14.137{cm}^{3}


Assuming the marble has an spherical shape, its volume can be calculated by the following formula:


V_{sphere}=\frac{4}{3}\pi{r}^{3}     (1)


where r is the radius of the sphere and also is the half of its diameter d:


r=\frac{d}{2}     (2)


Now, if we know the diameter of the black marble is 3cm, its radius is:


r=\frac{3}{2}cm     (3)


Substituting this value on equation (1):


V_{sphere}=\frac{4}{3}\pi{(\frac{3}{2}cm)}^{3}


Simplifying:

V_{sphere}=\frac{9}{2}\pi{cm}^{3}


V_{sphere}=14.137{cm}^{3}>>>>>This is an approximation of the volume of the marble


Note that 1{cm}^{3}=1ml, therefore the result above can be also written as 14.137ml


2. Answer: 64.137 ml


According to the Archimedes’ Principle a body totally or partially immersed in a fluid at rest, experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.


In this case, if we have a graduated cylinder with the capacity to contain 100 ml of water, and we fill it with 50 ml of water (as shown in the image attached) and then we add the black marble until it sinks; the water level will increase according to the principle explained above.

As the marble does not absorb water, the space it occupies displaces the water upwards and, in this way, it is possible to determine its volume or the final volume the water level indicates in the cylinder.


We already know the initial volume of water V_i in the graduated cylinder, which is 50 ml, and we know the volume of the marble V_m because we calculated it above. If we want to know the final volume of water level V_f we have to use the following relation:


V_{f}-V_{i}=V_{m}     (4)


and find V_f:


V_{f}=V_{i}+V_{m}     (5)


V_{f}=50ml+14,137ml    


Finally:

V_{f}=64,137ml>>>>>This is the final volume of the water level indicated in the graduated cylinder




Luden [163]3 years ago
7 0

the answer is 14cm

and 124mL

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