Calculating Mass Density of a Steel Sphere | Help Needed!

[derivethis]

Hi all! This is my first post here. I have a question regarding how to calculate the mass density of a steel sphere. Any help is much appreciated!

Homework Statement

The mass of the sphere is equal to 8.4 grams. The volume of the sphere is equal to 1060 cm^3.

Homework Equations

The mass was found during our lab experiment. The volume was calculated from the equation: V = (4/3) pi R^3. The diameter of the sphere was 12.65 cm. Therefore, I calculated the volume as follows: (4/3) pi (12.65/2)^3 = 1060 cm^3.

The Attempt at a Solution

Mass density is equal to mass/volume; therefore it should be 8.4g/1060cm^3 = 0.0079gm/cm^3. However, I'm also supposed to calculate the percent error for my lab report, and the "true" value for the mass density of steel is given as 7.9 gm/cm^3. Percent error is equal to (|Accepted - Measured|)/Accepted * 100, which, in this case, would be (|7.9 - 0.0079|)/7.9 * 100 = 99.9%. This gives me a percent error of almost 100%! What am I doing wrong in my calculations? Please help! Thank you!

 

[l'Hôpital]

Are you sure you have your units right?

1 gram = 10^-3 kg. And 1 cm^3 = 10^-6 m^3.

so 1 g/cm^3 = 10^-3 / 10^-6 kg/m^3 = 10^3 kg/cm

so your 0.0079 g/cm^3 = 7.9 kg/m^3.

 

[vela]

Your volume is about 1000 cm³, which is 1 liter. Does that sound right?

 

[derivethis]

Thank you for your replies!

l'Hôpital: I think that I'm supposed to keep the units in grams/cm^3. I think my lab group and I must have made some sort of error in lab, which, of course, I can't correct now. We had to use a micrometer to determine the diameter of the steel sphere, and I just now realized that there's no way that the diameter of the sphere was 12.65 centimeters since the sphere was tiny and 1 inch = 2.54 cm. Hmm ... I wonder if it should be 12.65 mm instead. I believe that when we used the micrometer, we had to take it out to the number 10 mark in order for the sphere to fit inside. Does anyone know what this means? Thank you!

 

[diazona]

Thank you for your replies!

l'Hôpital: I think that I'm supposed to keep the units in grams/cm^3. I think my lab group and I must have made some sort of error in lab, which, of course, I can't correct now. We had to use a micrometer to determine the diameter of the steel sphere, and I just now realized that there's no way that the diameter of the sphere was 12.65 centimeters since the sphere was tiny and 1 inch = 2.54 cm. Hmm ... I wonder if it should be 12.65 mm instead. I believe that when we used the micrometer, we had to take it out to the number 10 mark in order for the sphere to fit inside. Does anyone know what this means? Thank you!

That doesn't really tell us much unless we would have access to the same kind of micrometer you used.

There's a decent chance that your measurement of the diameter was off by a factor of 10 - that's a relatively common mistake to make. So it might have been 12.65mm. Based on your memory of what the sphere looked like, does 12.65mm seem like a reasonable value for its diameter? If so, try recalculating the density using that diameter and see what you get.