Volume of Secret Compartment in Brass Sculpture

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The discussion centers on calculating the volume of a secret compartment in a brass sculpture based on its weight in air and water. The initial calculations mistakenly treated the volumes as separate, leading to incorrect results. The correct approach involves using the difference in weight when submerged to determine the volume of water displaced, which corresponds to the volume of the secret cavity. The final calculations yield a volume of approximately 2 x 10^-4 m^3 for the compartment. This method effectively clarifies the relationship between weight, volume, and density in the context of the sculpture.
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A small sculpture made of brass (p = 8470 kg/m^3) is believed to have a secret central cavity. The weight of teh sculpture in air is 15.76N. When it is submerged in water, the weight is 13.86N. What is the volume of the secret compartment?

Fb = W
W = pgV

15.76 = 8470 * 9.8 * V
15.76 = 83006V
1.89x10^-4 = V

13.86 = 8470 * 9.8 * V
13.86 = 83006V
1.66x10^-4 = V

1.89x10^-4 - 1.66x10^-4 = 2.3x10^-6

This is wrong. Why?
 
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Wrong calculation: 1.89x10^-4 - 1.66x10^-4 = 2.3x10^-5.
 
I don't understand what you've done - you appear to have calculated 2 volumes. The volume is constant.

Remember, the mass (weight) difference in water tells you the mass (weight) of water displaced. So use this to find the volume of water displaced - then you know the volume of the whole brass thing.

Calculate what a SOLID brass thing of this volume should weigh.

Find the "missing" mass or weight then the volume.

There might be a quicker way. ...
 
Ah - you worked out the whole volume then the volume of just brass?

But did it work?
 
What I did is find the volume of the brass in the air, then the volume in the water and found the difference between the two. This is not the correct answer though. What did I do wrong?
 
OK, think I got it now:

V= m/p

Air = 15.76 / 8470
= 1.8 x 10^-3

Water = 13.86 / 8470
= 1.6x10^-3

Difference of the two is 2x10^-4, which happens to be one of the answers.
 
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